HANSEN MEDICAL, INC. FORM OF SERIES [A][B][C] WARRANT

Exhibit 4.1

NEITHER THIS WARRANT, NOR THE SECURITIES ISSUABLE UPON EXERCISE OF THIS WARRANT (COLLECTIVELY, THE “SECURITIES”), HAVE BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE “SECURITIES ACT”), OR UNDER ANY STATE SECURITIES OR BLUE SKY LAWS. THE SECURITIES ARE SUBJECT TO RESTRICTIONS ON TRANSFERABILITY AND RESALE AND MAY NOT BE OFFERED, SOLD, PLEDGED, HYPOTHECATED OR OTHERWISE TRANSFERRED EXCEPT AS PERMITTED UNDER THE SECURITIES ACT AND APPLICABLE STATE SECURITIES OR BLUE SKY LAWS, PURSUANT TO REGISTRATION OR QUALIFICATION OR EXEMPTION THEREFROM. INVESTORS SHOULD BE AWARE THAT THEY MAY BE REQUIRED TO BEAR THE FINANCIAL RISKS OF THIS INVESTMENT FOR AN INDEFINITE PERIOD OF TIME. THE ISSUER OF THE SECURITIES MAY REQUIRE AN OPINION OF COUNSEL IN FORM AND SUBSTANCE REASONABLY SATISFACTORY TO THE ISSUER TO THE EFFECT THAT ANY PROPOSED TRANSFER IS IN COMPLIANCE WITH THE SECURITIES ACT AND ANY APPLICABLE STATE SECURITIES OR BLUE SKY LAWS. THIS WARRANT IS SUBJECT TO THE TRANSFER RESTRICTIONS SET FORTH HEREIN AND IN AN INVESTORS RIGHT AGREEMENT, DATED AS OF [—], 2013, COPIES OF WHICH ARE AVAILABLE WITH THE SECRETARY OF THE ISSUER.

HANSEN MEDICAL, INC.

FORM OF SERIES [A][B][C] WARRANT

Hansen Medical, Inc., a Delaware corporation (the “Company”), hereby certifies that, for value received, [—], a [—], or its registered assign (the “Holder”), is entitled to purchase from the Company [—] shares (as adjusted from time to time as provided in Section 12) of common stock, par value $0.0001 per share, of the Company (the “Common Stock”) (each such share, a “Warrant Share” and all such shares, the “Warrant Shares”), at an exercise price determined pursuant to Section 3 (the “Exercise Price”), at any time and from time to time from and after the date hereof through and including the date that is two (2) years following the date of issuance set forth above (the “Expiration Date”), and subject to the following terms and conditions:

1. Purchase Agreement. This Series [A][B][C] Warrant (this “Warrant”) is one of a series of Warrants (collectively, the “Warrants”) issued by the Company in connection with that certain Securities Purchase Agreement, entered into on July 30, 2013 (the “Purchase Agreement”), by and among the Company and Holder and certain other Purchasers, and is subject to, and the Company and the Holder shall be bound by, all the applicable terms, conditions and provisions of the Purchase Agreement.

2. Definitions. In addition to the terms defined elsewhere in this Warrant, capitalized terms that are not otherwise defined herein shall have the meanings assigned to such terms in the Purchase Agreement.

3. Exercise Price. This Warrant may be exercised for a price per Warrant Share equal to $[—]², subject to adjustment from time to time pursuant to Section 12 (the “Exercise Price”).

4. Registration of Warrant. The Company shall register this Warrant, upon records to be maintained by the Company for that purpose (the “Warrant Register”), in the name of the record Holder hereof from time to time. The Company may deem and treat the Holder of this Warrant as the absolute owner hereof for the purpose of any exercise hereof or any distribution to the Holder, and for all other purposes, absent actual notice to the contrary.

5. Transfer of Warrant.

(a) No Holder may, directly or indirectly, sell, exchange, assign or otherwise transfer all or any portion of this Warrant without the prior written consent of the Company; provided that (i) a Holder that is a natural person may transfer all or a portion of this Warrant to one or more trusts for the benefit of such Holder, such Holder’s spouse, a lineal descendant of such Holder or such Holder’s parents, the spouse of any such descendant or a lineal descendant of any such spouse and (ii) a Holder that is a Person other than a natural person may transfer all or a portion of the Warrant to an Affiliate of such Holder.

(b) Subject to the Holder’s appropriate compliance with the restrictive legend on this Warrant and the transfer restrictions set forth herein, the Company shall register the transfer of any portion of this Warrant in the Warrant Register, upon surrender of this Warrant, with the Form of Assignment substantially in the form attached hereto as Attachment B duly completed and signed, to the Company at its address specified herein. Upon any such registration or transfer, a new Warrant to purchase Common Stock, in substantially the form of this Warrant (any such new Warrant, a “New Warrant”), evidencing the portion of this Warrant so transferred shall be issued to the transferee and a New Warrant evidencing the remaining portion of this Warrant not so transferred, if any, shall be issued to the transferring Holder. The acceptance of the New Warrant by the transferee thereof shall be deemed the acceptance by such transferee of all of the rights and obligations of a holder of a Warrant.

6. Exercise and Duration of Warrants. This Warrant shall be exercisable by the registered Holder at any time and from time to time on or after the date hereof to and including the Expiration Date. At 6:30 p.m., New York City time, on the Expiration Date, the portion of this Warrant not exercised prior thereto shall be and become void and of no value. [The Company may not call or redeem all or any portion of this Warrant without the prior written consent of the Holder.]³ [The Company shall notify the Holder in writing of the occurrence of regulatory approval by the U.S. Food and Drug Administration of the Hansen Medical 6F Magellan Catheter in the United States (the “Milestone Event”), with such notification to be accompanied by a certification executed by the Chief Financial Officer of the Company as to the occurrence of the Milestone Event. Within fifteen (15) days after receipt of such Company notice, the Holder shall exercise this Warrant in full by paying the price per Warrant Share equal to the Exercise Price.]⁴

7. Delivery of Warrant Shares.

(a) To effect conversions hereunder, the Holder shall not be required to physically surrender this Warrant unless the aggregate number of Warrant Shares represented by this Warrant is being exercised. Upon delivery of an Exercise Notice substantially in the form attached hereto as Attachment A (an “Exercise Notice”) to the Company at its address for notice determined as set forth herein, and upon payment of the applicable Exercise Price multiplied by the number of Warrant Shares that the Holder intends to purchase hereunder, the Company shall promptly (but in no event later than five

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(5) trading days after the Date of Exercise (as defined below)) issue and deliver, or cause its transfer agent to issue and deliver, to the Holder a certificate for the Warrant Shares issuable upon such exercise registered in the name of the Holder or its designee. A “Date of Exercise” means the date on which the Holder shall have delivered to the Company: (i) an Exercise Notice, appropriately completed and duly signed, and (ii) payment of the Exercise Price (by certified or official bank check, intra-bank account transfer or wire transfer) for the number of Warrant Shares so indicated by the Holder to be purchased.

(b) If by the fifth trading day after a Date of Exercise the Company fails to deliver the required number of Warrant Shares in the manner required pursuant to Section 7(a), the Holder will have the right to rescind such exercise.

(c) The Company’s obligations to issue and deliver Warrant Shares in accordance with the terms hereof are absolute and unconditional, irrespective of any action or inaction by the Holder to enforce the same, any waiver or consent with respect to any provision hereof, the recovery of any judgment against any Person or any action to enforce the same, or any setoff, counterclaim, recoupment, limitation or termination, or any breach or alleged breach by the Holder or any other Person of any obligation to the Company or any violation or alleged violation of law by the Holder or any other Person, and irrespective of any other circumstance which might otherwise limit such obligation of the Company to the Holder in connection with the issuance of Warrant Shares. Nothing herein shall limit a Holder’s right to pursue any other remedies available to it hereunder, at law or in equity, including a decree of specific performance and/or injunctive relief with respect to the Company’s failure to timely deliver certificates representing shares of Common Stock upon exercise of the Warrant as required pursuant to the terms hereof.

8. Charges, Taxes and Expenses. Issuance and delivery of certificated or uncertificated shares of Common Stock upon exercise of this Warrant shall be made without charge to the Holder for any issue or transfer tax, withholding tax, transfer agent fee, or other incidental tax or expense in respect of the issuance of such shares, all of which taxes and expenses shall be paid by the Company; provided, however, that the Company shall not be required to pay any tax which may be payable in respect of any transfer involved in the registration of any certificates for Warrant Shares or Warrants in a name other than that of the Holder. The Holder shall be responsible for all other tax liability that may arise as a result of holding or transferring this Warrant or receiving Warrant Shares upon exercise hereof.

9. Replacement of Warrant. If this Warrant is mutilated, lost, stolen or destroyed, the Company shall issue or cause to be issued in exchange and substitution for and upon cancellation hereof, or in lieu of and substitution for this Warrant, a new Warrant, but only upon receipt of evidence reasonably satisfactory to the Company of such loss, theft or destruction and customary and reasonable indemnity (which shall not include a surety bond), if requested. Applicants for a new warrant under such circumstances shall also comply with such other reasonable regulations and procedures and pay such other reasonable third-party costs as the Company may prescribe. If a new warrant is requested as a result of a mutilation of this Warrant, then the Holder shall deliver this mutilated Warrant to the Company as a condition precedent to the Company’s obligation to issue the new warrant.

10. Reservation of Warrant Shares. The Company covenants that it will at all times reserve and keep available out of the aggregate of its authorized but unissued and otherwise unreserved Common Stock, solely for the purpose of enabling it to issue Warrant Shares upon exercise of this Warrant as herein provided, the number of Warrant Shares which are then issuable and deliverable upon the exercise of this entire Warrant, free from Liens or any other contingent purchase rights of persons other than the Holder (taking into account the adjustments and restrictions of Section 12). The Company covenants and warrants that all Warrant Shares so issuable and deliverable shall, upon issuance and the payment of the applicable Exercise Price in accordance with the terms hereof, be duly and validly authorized, issued and fully paid and non-assessable.

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11. Notice of Certain Corporate Action. In case the Company shall propose (a) to offer to the holders of its Common Stock rights to subscribe for or to purchase any shares of Common Stock or shares of stock of any class or any other securities, rights or options, or (b) to effect any reclassification of its Common Stock (other than a reclassification involving only the subdivision, or combination, of outstanding shares of Common Stock), or (c) to effect any capital reorganization, or (d) to effect any Fundamental Transaction (as defined below), or (e) to effect the liquidation, dissolution or winding up of the Company or (f) to offer to the holders generally of its Common Stock the right to have their shares of Common Stock repurchased or redeemed or otherwise acquired by the Company, or (g) to take any other action which would require the adjustment of the Exercise Price and/or the number of Warrant Shares issuable upon exercise of this Warrant, then in each such case (but without limiting the provisions of Section 12), the Company shall give to the Holder, a notice of such proposed action, which shall specify the date on which a record is to be taken for purposes of such dividend, distribution of offer of rights, or the date on which such reclassification, reorganization, Fundamental Transaction, liquidation, dissolution, or winding up is to take place and the date of participation therein by the holders of Common Stock, if any such date is to be fixed and shall also set forth such facts with respect thereto as shall be reasonably necessary to indicate the effect of such action on the Common Stock. Such notice shall be so given at least ten (10) Business Days prior to the record date for determining holders of the Common Stock for purposes of participating in or voting on such action, or at least ten (10) Business Days prior to the date of the taking of such proposed action or the date of participation therein by the holders of Common Stock, whichever shall be the earlier. Such notice shall specify, in the case of any subscription or repurchase rights, the date on which the holders of Common Stock shall be entitled thereto, or the date on which the holders of Common Stock shall be entitled to exchange their Common Stock for securities or other property deliverable upon any reorganization, reclassification, Fundamental Transaction or other action, as the case may be. Such notice shall also state whether the action in question or the record date is subject to the effectiveness of a registration statement under the Securities Act or to a favorable vote of security holders, if either is required, and the adjustment in Exercise Price and/or number of Warrant Shares issuable upon exercise of this Warrant as a result of such reorganization, reclassification, Fundamental Transaction or other action, to the extent then determinable. No such notice shall be given if the Company reasonably determines that the giving of such notice would require disclosure of material information which the Company has a bona fide purpose for preserving as confidential or the disclosure of which would not be in the best interests of the Company.

12. Certain Adjustments. The number of Warrant Shares issuable upon exercise of this Warrant is subject to adjustment from time to time as set forth in this Section 12.

(a) Stock Dividends and Splits. If the Company, at any time while this Warrant is outstanding: (i) pays a stock dividend or otherwise makes a distribution or distributions on shares of its Common Stock or any other equity or equity equivalent securities payable in shares of Common Stock (which, for avoidance of doubt, shall not include any shares of Common Stock issued by the Company upon exercise of any Warrants), (ii) subdivides outstanding shares of Common Stock into a larger number of shares, (iii) combines (including by way of reverse stock split) outstanding shares of Common Stock into a smaller number of shares, or (iv) issues by reclassification of shares of Common Stock any shares of capital stock of the Company; then in each such case (A) the Exercise Price will be adjusted by multiplying the Exercise Price then in effect by a fraction, the numerator of which equals the number of shares of Common Stock outstanding immediately prior to such event (excluding treasury shares, if any), and the denominator of which equals the number of shares of Common Stock outstanding immediately after such event (excluding treasury shares, if any), and (B) the number of Warrant Shares issuable hereunder shall be concurrently adjusted by multiplying such number by the reciprocal of such fraction.

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Such adjustments will take effect (i) if a record date shall have been fixed for determining the stockholders or security holders, as applicable, of the Company entitled to receive such dividend, distribution or issuance by reclassification, as the case may be, immediately after such record date, (ii) otherwise, immediately after the effective date of such dividend, distribution, subdivision, combination, or issuance by reclassification, as the case may be.

(b) Fundamental Transaction. If, at any time while this Warrant is outstanding, (i) the Company, directly or indirectly, in one or a series of related transactions, (A) effects any merger or consolidation of the Company with or into another Person, (B) effects any sale, lease, license, assignment, transfer, conveyance or other disposition of all or substantially all of its assets, (C) effects any reclassification, reorganization or recapitalization of the Common Stock or any compulsory share exchange pursuant to which the Common Stock is effectively converted into or exchanged for other securities, cash or property (except for issuances by reclassification contemplated by Section 12(a)(iv)), or (D) consummates a stock or share purchase agreement or other business combination (including a reorganization, recapitalization, spin-off or scheme of arrangement) with another Person or group of Persons whereby such other Person or group acquires more than fifty percent (50%) of the outstanding shares of Common Stock (not including any shares of Common Stock held by the other Person or group making or party to, or associated or affiliated with the other Persons making or party to, such stock or share purchase agreement or other business combination), or (ii) any, direct or indirect, purchase offer, tender offer or exchange offer (whether by the Company or another Person or group of Persons) is completed pursuant to which holders of Common Stock are permitted to sell, tender or exchange their shares for other securities, cash or property (each transaction or series of transactions referred to in clause (i) or (ii) above, a “Fundamental Transaction”); then, upon any subsequent exercise of this Warrant, the Holder shall have the right to receive, for each Warrant Share that would have been issuable upon such exercise immediately prior to the occurrence of such Fundamental Transaction, (1) the number of shares of common stock of the successor or acquiring corporation or, if it is the surviving corporation, of the Company, and (2) any additional consideration (the “Alternate Consideration”) receivable as a result of such Fundamental Transaction by a holder of the number of shares of Common Stock for which this Warrant is exercisable immediately prior to such Fundamental Transaction. For purposes of any such exercise, the determination of the Exercise Price shall be appropriately adjusted to apply to such Alternate Consideration based on the amount and components of Alternate Consideration issuable in respect of one share of Common Stock in such Fundamental Transaction, and the Board shall apportion the Exercise Price among the Alternate Consideration in a reasonable manner reflecting the relative value of any different components of the Alternate Consideration (substituting the most appropriate market-based measure for the Trading Market in determining the daily VWAP from time to time for each component of the Alternate Consideration or, if no market-based measure is reasonably available for any such component, fixing the daily VWAP of such component at the value determined by such apportionment, but subject to further adjustment as provided in this Section 12). If holders of Common Stock are given any choice as to the securities, cash or property to be received in a Fundamental Transaction, then the Holder shall be given the same choice as to the Alternate Consideration it receives upon any exercise of this Warrant following such Fundamental Transaction. To the extent necessary to effectuate the foregoing provisions, any successor to the Company or surviving entity in such Fundamental Transaction shall issue to the Holder a new warrant of like tenor to this Warrant but adjusted to be consistent with the foregoing provisions and evidencing the Holder’s right to exercise such warrant for the appropriate number of shares of capital stock and Alternate Consideration, if any, in exchange for this Warrant. The Company shall ensure that the terms of any agreement pursuant to which a Fundamental Transaction is effected shall include terms requiring any such successor or surviving entity to comply with the provisions of this Section 12(b) and ensuring that this Warrant (or any such replacement security) will be similarly adjusted upon any subsequent transaction or series of related transactions analogous to a Fundamental Transaction. “VWAP” means, for any date, the price determined by the first of the following clauses that applies: (A) if the Common Stock is then listed or quoted on a trading market, the

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daily volume weighted average price of the Common Stock for such date (or the nearest preceding date) on the principal trading market on which the Common Stock is then listed or quoted as reported by Bloomberg L.P. (based on a trading day from 9:30 a.m. (New York City time) to 4:02 p.m. (New York City time)), (B) if prices for the Common Stock are then reported in the “Pink Sheets” published by Pink OTC Markets, Inc. (or a similar organization or agency succeeding to its functions of reporting prices), the most recent bid price per share of the Common Stock so reported during trading hours, or (C) in all other cases, the fair market value of a share of Common Stock as determined by an independent appraiser selected in good faith by the Company’s Board of Directors and reasonably acceptable to the Holder, the fees and expenses of which shall be paid by the Company.

(c) Notice of Adjustment. Upon any adjustment of the Exercise Price, and from time to time upon the request of the Holder, the Company shall furnish to the Holder the Exercise Price resulting from such adjustment or otherwise in effect and the number of Warrant Shares then available for purchase under this Warrant, setting forth in reasonable detail the method of calculation and the facts upon which such calculation is based.

13. No Fractional Shares. No fractional shares of Common Stock will be issued in connection with any exercise of this Warrant. In lieu of any fractional shares which would otherwise be issuable, the Company shall pay the Holder an amount of cash equal to the product of such fraction multiplied by the closing price of one share of Common Stock as reported on the principal trading market for the Common Stock on the Date of Exercise.

14. No Impairment. The Company shall not by any action including, without limitation, amending its Certificate of Incorporation, any reorganization, transfer of assets, consolidation, merger, dissolution, issue or sale of securities or any other voluntary action, avoid or seek to avoid the observance or performance of any of the terms of this Warrant, but shall at all times in good faith assist in the carrying out of all such terms and in the taking of all such action, as may be necessary or appropriate to protect the rights of the Holder against impairment. Without limiting the generality of the foregoing, the Company shall take all such action as may be necessary or appropriate in order that the Company may validly issue fully paid and nonassessable shares of Common Stock upon the exercise of this Warrant at the then Exercise Price therefor.

15. No Rights as a Stockholder; Notice to Holder. Nothing contained in this Warrant shall be construed as conferring upon the Holder the right to vote or to consent or to receive notice as a stockholder in respect of any meeting of stockholders for the election of directors of the Company or any other matter, or any rights whatsoever as a stockholder of the Company.

16. Warrant Agent. The Company shall serve as warrant agent under this Warrant. Upon thirty (30) days notice to the Holder, the Company may appoint a new warrant agent. Any corporation into which the Company or any new warrant agent may be merged or any corporation resulting from any consolidation to which the Company or any new warrant agent shall be a party or any corporation to which the Company or any new warrant agent transfers substantially all of its corporate trust or stockholders services business shall be a successor warrant agent under this Warrant without any further act. Any such successor warrant agent shall promptly cause notice of its succession as warrant agent to be mailed (by first class mail, postage prepaid) to the Holder at the Holder’s last address as shown on the Warrant Register.

17. Miscellaneous.

(a) Notices. Any and all notices or other communications or deliveries hereunder (including any Exercise Notice) shall be in writing and shall be deemed given and effective on the earliest

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of (i) the date of transmission, if such notice or communication is delivered via facsimile at the facsimile number pursuant to this Section 17(a) prior to 5:30 p.m. (New York City time) on a trading day, (ii) the next trading day after the date of transmission, if such notice or communication is delivered via facsimile at the facsimile number specified pursuant to this Section 17(a) on a day that is not a trading day or later than 5:30 p.m. (New York City time) on any trading day, (iii) the second trading day following the date of mailing, if sent by nationally recognized overnight courier service to the street address specified pursuant to this Section 17(a), or (iv) upon actual receipt by the party to whom such notice is required to be given. The addresses for such communications shall be as follows:

(i) if to the Company, to:

Hansen Medical, Inc.

800 East Middlefield Road

Mountain View, CA 94043

Attn: Chief Financial Officer

Facsimile: (650)  ###-###-####

with a copy to (which shall not constitute notice to the Company):

Skadden, Arps, Slate, Meagher & Flom LLP

525 University Avenue Suite 1400

Palo Alto, CA 94301

Attn: Thomas J. Ivey

Facsimile: (650)  ###-###-####

(ii) if to the Holder, to the address, facsimile number or email or street address appearing on the Warrant Register (which shall initially be the facsimile number and email and street address set forth for the initial Holder in the Purchase Agreement);

or to such other address, facsimile number or email address as the Company or the Holder may provide to the other in accordance with this Section 17(a).

(b) Assignment. Subject to the restrictions on transfer described herein, the rights and obligations of the Company and the Holder shall be binding upon, and inure to the benefit of, the successors, assigns, heirs, administrators and transferees of the parties. The Company shall not have the right directly or indirectly to assign or transfer this Warrant without the prior written consent of the Holder, which may be withheld in the Holder’s sole discretion, or as part of a Fundamental Transaction.

(c) No Third Party Beneficiaries. Nothing in this Warrant shall be construed to give to any Person other than the Company and the Holder any legal or equitable right, remedy or cause of action under this Warrant.

(d) Amendments; Waiver. This Warrant may be amended only in writing signed by the Company and the Holder, and any amendment so effected shall amend each Warrant issued pursuant to the Purchase Agreement and be binding upon each holder of such Warrants (provided, however, that any such amendment that adversely affects any holder or class of holders of such Warrants in a manner that does not apply uniformly to all holders of such Warrants, as applicable, shall require the written consent of such adversely affected holders or class). Any provision of this Warrant may be waived, but only if in writing by the party against whom enforcement of any such waiver is sought. No waiver of any default with respect to any provision, condition or requirement of this Warrant shall be deemed to be a continuing waiver in the future or a waiver of any subsequent default or a waiver of any other provision, condition or requirement hereof, nor shall any delay or omission of either party to exercise any right hereunder in any manner impair the exercise of any such right.

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(e) Governing Law. This Warrant shall be governed by and construed in accordance with the laws of the State of Delaware, without regard to principles of conflict of laws.

(f) Severability. If one or more provisions of this Warrant are held to be unenforceable under applicable law in any respect, such provision shall be excluded from this Warrant and the balance of this Warrant shall be construed and interpreted as if such provision were so excluded and shall be enforceable in accordance with its remaining terms.

[Remainder of Page Intentionally Left Blank; Signature Page Follows]

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IN WITNESS WHEREOF, the Company has caused this Warrant to be duly executed by its authorized officer as of the date first indicated above.

[Signature Page – Warrant]

ATTACHMENT A

EXERCISE NOTICE

To Hansen Medical, Inc.:

The undersigned hereby irrevocably elects to purchase shares (the “Shares”) of common stock, par value $0.0001 per share (“Common Stock”), of Hansen Medical, Inc., a Delaware corporation, pursuant to Warrant No. [A][B][C]-            , originally issued on                     , 2013 (the “Warrant”). The undersigned elects to utilize the following manner of exercise:

Shares:

[Please issue a new Warrant for the unexercised portion of the attached Warrant in the name of the [undersigned]/[the undersigned’s nominee as is specified below].]

ATTACHMENT B

FORM OF ASSIGNMENT

[To be completed and signed only upon transfer of Warrant]

FOR VALUE RECEIVED, the undersigned hereby sells, assigns and transfers unto                                  the right represented by the attached Series [A][B][C] Warrant to purchase              shares of Common Stock of Hansen Medical, Inc., a Delaware corporation (the “Company”), to which the Warrant relates and appoints                      as attorney to transfer said right on the books of the Company with full power of substitution in the premises.