EXHIBIT A

Exhibit 10.1

EXHIBIT A

WARRANT AGREEMENT

THIS WARRANT AGREEMENT is made as of July 26, 2005, by and between Fulton Financial Corporation, a Pennsylvania corporation (“Fulton”) and Columbia Bancorp, a Maryland corporation (“Columbia”).

WITNESSETH:

WHEREAS, Fulton and Columbia have entered into an Agreement and Plan of Merger, dated July 26, 2005 (the “Merger Agreement”); and

WHEREAS, in connection with Fulton’s entry into the Merger Agreement and in consideration of such entry, Columbia has agreed to issue to Fulton, on the terms and conditions set forth herein, a warrant entitling Fulton to purchase up to an aggregate of 1,881,809 shares of Columbia’s common stock, $.01 par value per share (the “Common Stock”);

NOW, THEREFORE, in consideration of the execution of the Merger Agreement and the premises herein contained, and intending to be legally bound, Fulton and Columbia agree as follows:

1. Issuance of Warrant. Concurrently with the execution of this Agreement, Columbia shall issue to Fulton a warrant in the form attached as Exhibit A hereto (the “Warrant”, which term as used herein shall include any warrant or warrants issued upon transfer or exchange of the original Warrant) to purchase up to 1,881,809 shares of Common Stock, subject to adjustment as provided in this Agreement and in the Warrant. The Warrant shall be exercisable at a purchase price of $37.26 per share, subject to adjustment as provided in the Warrant (the “Exercise Price”). So long as the Warrant is outstanding and unexercised, Columbia shall at all times maintain and reserve, free from preemptive rights, such number of authorized but unissued shares of Common Stock as may be necessary so that the Warrant may be exercised, without any additional authorization of Common Stock, after giving effect to all other options, warrants, convertible securities and other rights to acquire shares of Common Stock. Columbia represents and warrants that it has duly authorized the execution and delivery of the Warrant and this Agreement and the issuance of Common Stock upon exercise of the Warrant. Columbia covenants that the shares of Common Stock issuable upon exercise of the Warrant shall be, when so issued, duly authorized, validly issued, fully paid and nonassessable and subject to no preemptive rights. The Warrant and the shares of Common Stock to be issued upon exercise of the Warrant are hereinafter collectively referred to, from time to time, as the “Securities.” So long as the Warrant is owned by Fulton, the Warrant will in no event be exercised for more than that number of shares of Common Stock equal to 1,881,809 (subject to adjustment as provided in the Warrant) less the number of shares of Common Stock at the time owned by Fulton.

2. Assignment, Transfer, or Exercise of Warrant. Fulton will not sell, assign, transfer or exercise the Warrant, in whole or in part, without the prior written consent of Columbia except upon or after the occurrence of any of the following: (i) a breach of any

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representation, warranty, or covenant set forth in the Merger Agreement by Columbia which would permit a termination of the Merger Agreement by Fulton pursuant to Section 8.1(b)(i) thereof following an offer or filing described in subparagraph (iv) below; (ii) the failure of Columbia’s stockholders to approve the Merger Agreement at a meeting called for such purpose if at the time of such meeting there has been an announcement by any Person (other than Fulton) of an offer or proposal to acquire 25% or more of the Common Stock (before giving effect to any exercise of the Warrant), or to acquire, merge or consolidate with Columbia, or to purchase all or substantially all of Columbia’s assets (including, without limitation, any shares of any subsidiary of Columbia or all or substantially all of any such subsidiary’s assets) and, within ten business days after such announcement, the Board of Directors of Columbia either fails to recommend against acceptance of such offer by Columbia’s stockholders or takes no position with respect thereto; (iii) the acquisition by any Person of Beneficial Ownership of 25% or more of the Common Stock (before giving effect to any exercise of the Warrant); (iv) any Person (other than Fulton) shall have commenced a tender or exchange offer, or shall have filed an application with an appropriate bank regulatory authority with respect to a publicly announced offer, to purchase or acquire securities of Columbia such that, upon consummation of such offer, such Person would have Beneficial Ownership of 25% or more of the Common Stock (before giving effect to any exercise of the Warrant) and, within 12 months from such offer or filing, such person consummates an acquisition described in subparagraph (iii) above; (v) Columbia shall have entered into an agreement, letter of intent or other understanding (except for a confidentiality agreement which would be permitted by Section 5.7(a)(x) of the Merger Agreement) with any Person (other than Fulton) providing for such Person (A) to acquire, merge, consolidate or enter into a statutory share exchange with Columbia or to purchase all or substantially all of Columbia’s assets (including without limitation any shares of any subsidiary of Columbia or all or substantially all of any such subsidiary’s assets); or (B) to negotiate with Columbia with respect to any of the events or transactions mentioned in the preceding clause (A) except for those negotiations which would be permitted by Section 5.7(a)(y) of the Merger Agreement; or (vi) termination, or attempted termination, of the Merger Agreement by Columbia under Section 8.1(c)(iii) of the Merger Agreement. As used in this Paragraph 2, the terms “Beneficial Ownership” and “Person” shall have the respective meanings set forth in Paragraph 7(f). The Warrant shall terminate in accordance with its terms.

3. Registration Rights. If, at any time within two years after the Warrant may be exercised or sold, Columbia shall receive a written request therefor from Fulton, Columbia shall prepare and file a shelf registration statement (the “Registration Statement”) under the Securities Act of 1933, as amended (the “Securities Act”), covering the Warrant (provided that no such registration shall be required with respect to the Warrant following the termination of the Warrant in accordance with its terms) and/or the Common Stock issued or issuable upon exercise of the Warrant (the “Securities”), and shall use its best efforts to cause the Registration Statement to become effective and remain current for such period not in excess of 180 days from the day such registration statement first becomes effective as may be reasonably necessary to affect such sale or other disposition. Without the prior written consent of Fulton, neither Columbia nor any other holder of securities of Columbia may include such securities in the Registration Statement.

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4. Duties of Columbia upon Registration. If and whenever Columbia is required by the provisions of Paragraph 3 of this Agreement to effect the registration of any of the Securities under the Securities Act, Columbia shall:

(a) prepare and file with the Securities and Exchange Commission (the “SEC”) such amendments to the Registration Statement and supplements to the prospectus contained therein as may be necessary to keep the Registration Statement effective and current;

(b) furnish to Fulton and to the underwriters of the Securities being registered such reasonable number of copies of the Registration Statement, the preliminary prospectus and final prospectus contained therein, and such other documents as Fulton or such underwriters may reasonably request in order to facilitate the public offering of the Securities;

(c) use its best efforts to register or qualify the Securities covered by the Registration Statement under the state securities or blue sky laws of such jurisdictions as Fulton or such underwriters may reasonably request;

(d) notify Fulton, promptly after Columbia shall receive notice thereof, of the time when the Registration Statement has become effective or any supplement or amendment to any prospectus forming a part of the Registration Statement has been filed;

(e) notify Fulton promptly of any request by the SEC for the amending or supplementing of the Registration Statement or the prospectus contained therein, or for additional information;

(f) prepare and file with the SEC, promptly upon the request of Fulton, any amendments or supplements to the Registration Statement or the prospectus contained therein which, in the opinion of counsel for Fulton, are required under the Securities Act or the rules and regulations promulgated by the SEC thereunder in connection with the public offering of the Securities;

(g) prepare and promptly file with the SEC such amendments of or supplements to the Registration Statement or the prospectus contained therein as may be necessary to correct any statements or omissions if, at the time when a prospectus relating to such Securities is required to be delivered under the Securities Act, any event shall have occurred as the result of which such prospectus as then in effect would include an untrue statement of a material fact or would omit to state any material fact required to be stated therein or necessary in order to make the statements therein, in the light of the circumstances under which they were made, not misleading;

(h) advise Fulton, promptly after Columbia shall receive notice or obtain knowledge of the issuance of any stop order by the SEC suspending the effectiveness of the Registration Statement, or the initiation or threatening of any proceeding for that purpose, and promptly use its best efforts to prevent the issuance of any stop order or to obtain its withdrawal if such stop order should be issued; and

(i) at the request of Fulton, furnish on the date or dates provided for in the underwriting agreement: (i) an opinion or opinions of counsel for Columbia for the

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purposes of such registration, addressed to the underwriters and to Fulton, covering such matters as such underwriters and Fulton may reasonably request and as are customarily covered by issuer’s counsel at that time; and (ii) a letter or letters from the independent accountants for Columbia, addressed to the underwriters and to Fulton, covering such matters as such underwriters or Fulton may reasonably request, in which letters such accountants shall state (without limiting the generality of the foregoing) that they are independent accountants within the meaning of the Securities Act and that, in the opinion of such accountants, the financial statements and other financial data of Columbia included in the Registration Statement or any amendment or supplement thereto comply in all material respects with the applicable accounting requirements of the Securities Act.

5. Expenses of Registration. With respect to the registration requested pursuant to Paragraph 3 of this Agreement, (a) Columbia shall bear all registration, filing and NASD fees, printing and engraving expenses, fees and disbursements of its counsel and accountants and all legal fees and disbursements and other expenses of Columbia to comply with state securities or blue sky laws of any jurisdictions in which the Securities to be offered are to be registered or qualified; and (b) Fulton shall bear all fees and disbursements of its counsel and accountants, underwriting discounts and commissions, transfer taxes for Fulton and any other expenses incurred by Fulton.

6. Indemnification. In connection with any Registration Statement or any amendment or supplement thereto:

(a) Columbia shall indemnify and hold harmless Fulton, any underwriter (as defined in the Securities Act) for Fulton, and each person, if any, who controls Fulton or such underwriter (within the meaning of the Securities Act) from and against any and all loss, damage, liability, cost or expense to which Fulton or any such underwriter or controlling person may become subject under the Securities Act or otherwise, insofar as such loss, damage, liability, cost or expense arises out of or is caused by any untrue statement or alleged untrue statement of any material fact contained in the Registration Statement, any prospectus or preliminary prospectus contained therein or any amendment or supplement thereto, or arises out of or is based upon the omission or alleged omission to state therein a material fact required to be stated therein or necessary in order to make the statements therein, in light of the circumstances under which they were made, not misleading; provided, however, that Columbia will not be liable in any such case to the extent that any such loss, damage, liability, cost or expense arises out of or is based upon an untrue statement or alleged untrue statement or omission or alleged omission so made in conformity with information furnished by Fulton, such underwriter or such controlling person in writing specifically for use in the preparation thereof.

(b) Fulton shall indemnify and hold harmless Columbia, any underwriter (as defined in the Securities Act), and each person, if any, who controls Columbia or such underwriter (within the meaning of the Securities Act) from and against any and all loss, damage, liability, cost or expense to which Columbia or any such underwriter or controlling person may become subject under the Securities Act or otherwise, insofar as such loss, damage, liability, cost or expense arises out of or is caused by any untrue or alleged untrue statement of any material fact contained in the Registration Statement, any

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prospectus or preliminary prospectus contained therein or any amendment or supplement thereto, or arises out of or is based upon the omission or the alleged omission to state therein a material fact required to be stated therein or necessary in order to make the statements therein, in light of the circumstances in which they were made, not misleading, in each case to the extent, but only to the extent, that such untrue statement or alleged untrue statement or omission or alleged omission was so made in reliance upon and in conformity with written information furnished by Fulton specifically for use in the preparation thereof.

(c) Promptly after receipt by any party which is entitled to be indemnified, pursuant to the provisions of subparagraph (a) or (b) of this Paragraph 6, of any claim in writing or of notice of the commencement of any action involving the subject matter of the foregoing indemnity provisions, such indemnified party shall, if a claim in respect thereof is to be made against the indemnifying party pursuant to the provisions of subparagraph (a) or (b) of this Paragraph 6, promptly notify the indemnifying party of the receipt of such claim or notice of the commencement of such action, but the omission to so notify the indemnifying party will not relieve it from any liability which it may otherwise have to any indemnified party hereunder. In case any such action is brought against any indemnified party and it notifies the indemnifying party of the commencement thereof, the indemnifying party shall have the right to participate in and, to the extent that it may wish, jointly with any other indemnifying party similarly notified, to assume the defense thereof, with counsel satisfactory to such indemnified party; provided, however, that if the defendants in any action include both the indemnified party or parties and the indemnifying party and there is a conflict of interest which would prevent counsel for the indemnifying party from also representing any indemnified party, such indemnified party shall have the right to select separate counsel to participate in the defense of such indemnified party. After notice from the indemnifying party to such indemnified party of its election so to assume the defense thereof, the indemnifying party will not be liable to such indemnified party, pursuant to the provisions of subparagraph (a) or (b) of this Paragraph 6, for any legal or other expenses subsequently incurred by such indemnified party in connection with the defense thereof, other than reasonable costs of investigation, unless (i) such indemnified party shall have employed separate counsel in accordance with the provisions of the preceding sentence, (ii) the indemnifying party shall not have employed counsel satisfactory to the indemnified party to represent the indemnified party within a reasonable time after the notice of the commencement of the action, or (iii) the indemnifying party has authorized the employment of counsel for the indemnified party at the expense of the indemnifying party.

(d) If recovery is not available under the foregoing indemnification provisions, for any reason other than as specified therein, any party entitled to indemnification by the terms thereof shall be entitled to obtain contribution with respect to its liabilities and expenses, except to the extent that contribution is not permitted under Section 11(f) of the Securities Act. In determining the amount of contribution to which the respective parties are entitled there shall be considered the parties’ relative knowledge and access to information concerning the matter with respect to which the claim was asserted, the opportunity to correct and/or prevent any statement or omission, and any other equitable considerations appropriate under the circumstances. Fulton and Columbia agree that it would not be equitable if the amount of such contribution were determined by pro rata or per capita allocation even if the underwriters and Fulton as a group were considered a single entity for such purpose.

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7. Redemption and Repurchase Rights.

(a) From and after the date on which any event described in Paragraph 2 of this Agreement occurs which permits the exercise of the Warrant, the Holder as defined in the Warrant (which shall include a former Holder), who has exercised the Warrant in whole or in part shall have the right to require Columbia to redeem some or all of the shares of Common Stock for which the Warrant was exercised at a redemption price per share (the “Redemption Price”) equal to the highest of: (i) 110% of the Exercise Price, (ii) the highest price paid or agreed to be paid for any share of Common Stock by an Acquiring Person (as defined below) during the one year period immediately preceding the date of redemption, and (iii) in the event of a sale of all or substantially all of Columbia’s assets or all or substantially all of a subsidiary of Columbia’s assets: (x) the sum of the price paid in such sale for such assets and the current market value of the remaining assets of Columbia as determined by a recognized investment banking firm selected by such Holder, divided by (y) the number of shares of Common Stock then outstanding. If the price paid consists in whole or in part of securities or assets other than cash, the value of such securities or assets shall be their then current market value as determined by a recognized investment banking firm selected by the Holder and reasonably acceptable to Columbia.

(b) From and after the date on which any event described in Paragraph 2 of this Agreement occurs which permits the exercise of the Warrant, the Holder as defined in the Warrant (which shall include a former Holder), shall have the right to require Columbia to repurchase all or any portion of the Warrant at a price (the “Warrant Repurchase Price”) equal to the product obtained by multiplying: (i) the number of shares of Common Stock represented by the portion of the Warrant that the Holder is requiring Columbia to repurchase, times (ii) the excess of the Redemption Price over the Exercise Price.

(c) The Holder’s right, pursuant to this Paragraph 7, to require Columbia to repurchase a portion or all of the Warrant, and/or to require Columbia to redeem some or all of the shares of Common Stock for which the Warrant was exercised, shall expire on the close of business on the 60th day following the occurrence of any event described in Paragraph 2 which permits the exercise of the Warrant.

(d) The Holder may exercise its right, pursuant to this Paragraph 7, to require Columbia to repurchase all or a portion of the Warrant, and/or to require Columbia to redeem some or all of the shares of Common Stock for which the Warrant was exercised, by surrendering for such purpose to Columbia, at its principal office within the time period specified in the preceding subparagraph, the Warrant and/or a certificate or certificates representing the number of shares to be redeemed accompanied by a written notice stating that it elects to require Columbia to repurchase the Warrant or a portion thereof and/or to redeem all or a specified number of such shares in accordance with the provisions of this Paragraph 7. As promptly as practicable, and in any event within five business days after the surrender of the Warrant and/or such certificates and the receipt of such notice

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relating thereto, Columbia shall deliver or cause to be delivered to the Holder: (i) the applicable Redemption Price (in immediately available funds) for the shares of Common Stock which it is not then prohibited under applicable law or regulation from redeeming, and/or (ii) the applicable Warrant Repurchase Price, and/or (iii) if the Holder has given Columbia notice that less than the whole Warrant is to be repurchased and/or less than the full number of shares of Common Stock evidenced by the surrendered certificate or certificates are to be redeemed, a new certificate or certificates, of like tenor, for the number of shares of Common Stock evidenced by such surrendered certificate or certificates less the number shares of Common Stock redeemed and/or a new Warrant reflecting the fact that only a portion of the Warrant was repurchased.

(e) To the extent that Columbia is prohibited under applicable law or regulation, or as a result of administrative or judicial action, from repurchasing the Warrant and/or redeeming the Common Stock as to which the Holder has given notice of repurchase and/or redemption, Columbia shall immediately so notify the Holder and thereafter deliver or cause to be delivered, from time to time to the Holder, the portion of the Warrant Repurchase Price and/or the Redemption Price which it is no longer prohibited from delivering, within five business days after the date on which Columbia is no longer so prohibited; provided, however, that to the extent that Columbia is at the time and after the expiration of 25 months, so prohibited from delivering the Warrant Repurchase Price and/or the Redemption Price, in full (and Columbia hereby undertakes to use its best efforts to obtain all required regulatory and legal approvals as promptly as practicable), Columbia shall deliver to the Holder a new Warrant (expiring one year after delivery) evidencing the right of the Holder to purchase that number of shares of Common Stock representing the portion of the Warrant which Columbia is then so prohibited from repurchasing, and/or Columbia shall deliver to the Holder a certificate for the shares of Common Stock which Columbia is then so prohibited from redeeming, and Columbia shall have no further obligation to repurchase such new Warrant or redeem such Common Stock; and provided further, that upon receipt of such notice and until five days thereafter the Holder may revoke its notice of repurchase of the Warrant and/or redemption of Common Stock by written notice to Columbia at its principal office stating that the Holder elects to revoke its election to exercise its right to require Columbia to repurchase the Warrant and/or redeem the Common Stock, whereupon Columbia will promptly redeliver to the Holder the Warrant and/or the certificates representing shares of Common Stock surrendered to Columbia for purposes of such repurchase and/or redemption, and Columbia shall have no further obligation to repurchase such Warrant and/or redeem such Common Stock.

(f) As used in this Agreement the following terms have the meanings indicated:

(1) “Acquiring Person” shall mean any “Person” (hereinafter defined) who or which is the “Beneficial Owner” (hereinafter defined) of 25% or more of the Common Stock (before giving effect to any exercise of the Warrant);

(2) A “Person” shall mean any individual, firm, corporation or other entity and shall also include any syndicate or group deemed to be a “Person” by operation of Section 13(d)(3) of the Securities Exchange Act of 1934, as amended;

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(3) A Person shall be a “Beneficial Owner”, and shall have “Beneficial Ownership,” of all securities:

(i) which such Person or any of its Affiliates (as hereinafter defined) beneficially owns, directly or indirectly; and

(ii) which such Person or any of its Affiliates or Associates has (1) the right to acquire (whether such right is exercisable immediately or only after the passage of time or otherwise) pursuant to any agreement, arrangement or understanding or upon the exercise of conversion rights, exchange rights, warrants or options, or otherwise, or (2) the right to vote pursuant to any proxy, power of attorney, voting trust, agreement, arrangement or understanding; and

(4) “Affiliate” and “Associate” shall have the respective meanings ascribed to such terms in Rule 12b-2 of the regulations promulgated by the SEC under the Securities and Exchange Act of 1934, as amended.

8. Remedies. Without limiting the foregoing or any remedies available to Fulton, it is specifically acknowledged that Fulton would not have an adequate remedy at law for any breach of this Warrant Agreement and shall be entitled to specific performance of Columbia’s obligations under, and injunctive relief against any actual or threatened violation of the obligations of any Person subject to, this Agreement.

9. Limitation of Holder’s Profit

(a) Notwithstanding any other provision of the Warrant, this Agreement or the Merger Agreement, in no event shall Holder’s Total Profit (as defined below) exceed $21,900,000 (“Maximum Profit”), and, if it otherwise would exceed such amount, Holder, at its sole discretion, shall either (i) reduce the number of shares subject to the Warrant, (ii) deliver to Columbia, for cancellation, shares of Common Stock, (iii) pay cash to Columbia, (iv) reduce the amount of the consideration paid pursuant to Section 7 of this Agreement or (v) any combination of the foregoing, so that Holder’s actually realized Total Profit shall not exceed the Maximum Profit after taking into account the foregoing actions. Notwithstanding any other provision of the Warrant, this Agreement or the Merger Agreement, the Warrant may not be exercised for a number of shares as would, as of the date of exercise, result in a Notional Total Profit (as defined below) of more than the Maximum Profit and, if exercise of the Warrant would otherwise result in the Notional Total Profit exceeding such amount, Holder, in its discretion, may take any of the actions specified in this Section 9(a) so that the Notional Total Profit shall not exceed the Maximum Profit; provided, however, that nothing in this sentence shall restrict any subsequent exercise of the Warrant which at such time complies with this sentence.

(b) For purposes of this Agreement, “Total Profit” shall mean: (i) the aggregate amount (before taxes) of (A) the excess of (x) the net cash amounts or fair market value of any property received by Holder pursuant to a sale of shares of Common Stock issued upon exercise of the Warrant (“Warrant Shares”), other than to a wholly-owned Subsidiary of Holder, or a repurchase of Warrant Shares by Columbia pursuant to Section 7

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of this Agreement, after payment of applicable brokerage or sales commissions and discounts, over (y) Holder’s aggregate purchase price for such Warrant Shares, plus (B) all amounts received by Holder upon the repurchase of the Warrant by Columbia pursuant to Section 7 of this Agreement, minus (ii) all amounts of cash previously paid to Columbia pursuant to Section 9(a) plus the value of the Warrant Shares previously delivered to Columbia for cancellation pursuant to Section 9(a), which value shall be deemed to be the aggregate Exercise Price paid for such Warrant Shares. For purposes of this Agreement, “Notional Total Profit” with respect to any number of shares as to which Holder may propose to exercise the Warrant shall be the Total Profit, determined as of the date of such proposed exercise assuming that the Warrant were exercised on such date for such number of shares, and assuming that such shares, together with all other Warrant Shares held by Holder and its affiliates as of such date, were sold for cash at the closing market price for the Common Stock as of the close of business on the preceding trading day (less customary brokerage commissions). For purposes of this Section 9, transactions by a wholly-owned Subsidiary transferee of Holder in respect of the Warrant or Warrant Shares transferred to it shall be treated as if made by Holder.

10. Miscellaneous.

(a) The representations, warranties, and covenants of Columbia set forth in the Merger Agreement are hereby incorporated by reference in and made a part of this Agreement, as if set forth in full herein.

(b) This Agreement, the Warrant and the Merger Agreement set forth the entire understanding and agreement of the parties hereto and supersede any and all prior agreements, arrangements and understandings, whether written or oral, relating to the subject matter hereof and thereof. No amendment, supplement, modification, waiver, or termination of this Agreement shall be valid and binding unless executed in writing by both parties.

(c) This Agreement shall be deemed to have been made in, and shall be governed by and interpreted in accordance with the substantive laws of, the Commonwealth of Pennsylvania.

(d) The covenants in this Agreement are severable, and if any covenant or portion thereof is held to be invalid or unenforceable for any reason, such covenant or portion thereof shall be modified or adjusted by a court or other tribunal exercising its equitable powers to the extent necessary to cure such invalidity or unenforceability, and all other covenants and provisions shall remain valid and enforceable.

[Signature Page Follows]

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IN WITNESS WHEREOF, the parties hereto have caused this instrument to be executed by their duly authorized officers as of the day and year first above written.

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