CONFIDENTIAL SEPARATION AGREEMENT AND GENERAL RELEASE OF CLAIMS

Exhibit 10.1

CONFIDENTIAL SEPARATION AGREEMENT

AND GENERAL RELEASE OF CLAIMS

This Agreement sets forth the agreement between Greater Bay Bancorp (the “Company”) and Steven C. Smith (“Smith”) regarding Smith’s retirement, and entitlement to employee benefits, from the Company.

The Company and Smith agree as follows:

1. Retirement from Office; Employment Termination; Consulting Agreement; Appointment to and Resignation from Board Memberships. Effective on the date specified in the next sentence (the “Retirement Date”), Smith shall retire from all positions he holds with the Company and each of its subsidiaries and affiliates and his employment with the Company and its subsidiaries and affiliates will terminate on that date. Smith agrees to continue in his employment with the Company until 30 days after the Company hires a replacement chief financial officer, but in no event later than December 31, 2003. At the beginning of such 30-day period, Smith shall resign as Chief Financial Officer and, during such period, he shall assist the new chief financial officer in a transitional capacity. Beginning on the day following the Retirement Date, Smith will provide consulting services to the Company pursuant to a Consulting Agreement in the form attached hereto as Exhibit A. On or before the Retirement Date, the Company will cause Smith to be appointed to the board of directors of its subsidiary Cupertino National Bank or, if Cupertino National Bank ceases to be a subsidiary of the Company, to the advisory board for its Cupertino National Bank subsidiary. Except for such membership on the board of directors or advisory board of Cupertino National Bank, effective as of the Retirement Date, Smith will resign from any and all board memberships, offices, trusteeships and management positions in which he serves on behalf of the Company’s subsidiaries and affiliated entities.

2. Bonus Compensation for 2003. If and when the Company pays its executive officers bonuses relating to 2003 performance (which, if bonuses are paid, is expected to be in or about February 2004), the Company shall pay Smith a bonus for 2003 in an amount based upon the performance of Smith and the Company during 2003 and prorated for the portion of 2003 that Smith was an employee of the Company.

3. Continuation of Benefits. Smith will continue to participate in the Company’s employee benefit programs, including the Greater Bay Bancorp 401(k) Plan and the Company’s group health insurance coverage and dental, life and disability insurance programs, through the Retirement Date. As of the day following the Retirement Date, Smith will no longer actively participate in the Company’s 401(k) Plan, and Smith will not be entitled to participate in any other Company employee benefit program, except to the extent expressly set forth in this Agreement and permitted under the documents governing such program. Smith will be entitled to receive retirement, life insurance and deferred compensation benefits that have accrued and vested on or before the Retirement Date in accordance with the terms and conditions of the plans or agreements applicable to such benefits. During the term of Smith’s membership on the board of directors and/or advisory board of Cupertino National Bank, he shall be entitled to continue to participate in the Company’s group health insurance coverage and dental, life and disability

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insurance programs on the same terms as apply to other nonemployee members of boards of directors and/or advisory boards of the Company’s subsidiaries. After Smith’s membership on the board of directors and/or advisory board of Cupertino National Bank has ended, and until Smith is eligible to enroll in Medicare, the Company will continue Smith’s participation in the Company’s group health insurance coverage, dental, life and disability insurance programs that are applicable to nonemployee directors, if and to the extent permissible under the documents governing such programs. Notwithstanding the foregoing, during the first 21 months following the Retirement Date, the Company shall pay the cost of Smith’s individual coverage under the Company’s group health insurance program, and any dependent coverage under such program will be provided on the same financial terms as apply from time to time to employees of the Company. After the first 21 months following the Retirement Date, any and all insurance coverage for Smith and his dependents shall be at Smith’s own expense. When Smith’s Company provided group health coverage ceases, Smith will be entitled to elect continued group health insurance coverage in accordance with applicable provisions of federal law (COBRA) at his own expense. On the Retirement Date, the Company shall make payment to Smith of all wages earned, including accrued but unused vacation, through the Retirement Date.

4. Stock Option Agreements. During his employment with the Company, Smith has participated in the Company’s 1996 Stock Option Plan, as amended. Smith’s rights under such plan and the agreements evidencing his prior stock option grants shall remain in full force and effect, and Smith shall continue to be entitled to receive the benefits specified therein in accordance with the terms and conditions of the plan and such agreements and this Agreement. Smith’s stock options under his prior stock option grants will continue to vest as though his Service (as such term is used in such plan and stock option agreements) continued for a period of 30 months following the Retirement Date and ended at that time, without regard to whether or not such Service in fact continues. This Agreement shall be considered to amend each of Smith’s stock option agreements in this respect. During the term of Smith’s membership on the board of directors and/or advisory board of Cupertino National Bank, he shall be given the same rights with respect to stock options as apply to other nonemployee members of boards of directors and/or advisory boards of the Company’s subsidiaries.

Smith understands that those of his stock options that are incentive stock options may become non-statutory options as a result of the arrangements set forth in this letter, the timing of their exercise or both. Smith also understands that he may recognize taxable income, equal to the “spread” on the option shares, if and when he exercises stock options that are or become non-statutory options, even if he does not then sell the option shares, and that the exercise of such stock options may then require withholding payments to tax authorities. Accordingly, consistent with Section 6(d) of the Company’s 1996 Stock Option Plan, as amended, and as a condition to the exercise of any stock option, in addition to the exercise price, Smith shall pay the Company (or make arrangements for payment satisfactory to the Company of) any and all federal, state and other tax withholding obligations that arise in connection with the exercise.

5. Release of Claims.

(a) In exchange for the payments and benefits described herein and in the Consulting Agreement, Smith releases the Company and its shareholders, subsidiaries, directors, employees, agents, attorneys, legal successors and assigns of and from any and all claims, actions and causes of action, whether now known or unknown, which Smith now has, or at any time had, or may

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have against the Company or any of such other persons based upon or arising out of any matter, cause, fact, thing, act or omission whatsoever occurring or existing at any time to and including the date hereof. This release specifically includes, but is not limited to, any and all claims under the Company’s Termination & Layoff Pay Plans and Change in Control Pay Plans; any claims for base or bonus compensation, severance pay, wages, benefits, wrongful termination, breach of contract, defamation, fraud, misrepresentation; any claims of discrimination based upon national origin, race, color, religion, age, sex, marital status, handicap, medical condition or other discrimination under the Civil Rights Act of 1964, the Age Discrimination In Employment Act of 1967 as amended by the Older Workers Benefit Protection Act, the Americans With Disabilities Act, the California Fair Employment and Housing Act, or any other applicable law; and any claims arising under and/or violations of any statutes, rules, regulations or ordinances whether federal, state or local, including, without limitation, the Employee Retirement Income Security Act of 1974, as amended (“ERISA”). As used in this Agreement, the term “Company” includes any and all parents, divisions, subsidiaries or affiliated entities of Greater Bay Bancorp.

(b) Smith acknowledges and agrees that he was provided 21 days to consider this Agreement and to consult with legal counsel and have the opportunity to receive independent legal advice with respect to the matters set forth in this Agreement and has been encouraged to do so. To the extent that Smith has taken less than 21 days to consider this Agreement, Smith acknowledges that Smith has had sufficient time to consider the Agreement and to consult with counsel and that Smith did not desire or need additional time.

(c) Smith may revoke this Agreement during the period of seven calendar days following Smith’s execution of this Agreement. The revocation must be in writing, must specifically revoke this Agreement, and must be directed to David Kalkbrenner at Greater Bay Bancorp, 400 Emerson Street, Palo Alto, California 94301, or faxed to him at facsimile number ###-###-####.

(d) Smith represents that he has not filed any notice, complaint or charges against the Company with any local, state or federal court or agency based upon events occurring prior to the date of execution of this Agreement. Smith agrees that he will not, in the future, file, instigate or encourage the filing of any proceeding or lawsuit by any party against the Company in any local, state or federal court or agency, except to the extent required to enforce Smith’s rights under this Agreement. Smith further agrees that he will not in the future cooperate or participate in any such lawsuit or proceedings except in accordance with this Agreement and as otherwise required by law.

6. Waiver of Statute and Release of Unknown Claims. Smith acknowledges that he has read section 1542 of the Civil Code of the State of California, which states:

A general release does not extend to claims which the creditor does not know or suspect to exist in his favor at the time of executing the release, which if known by him must have materially affected his settlement with the debtor.

Smith waives any right or benefit that he has under section 1542 of the Civil Code of the State of California to the full extent that Smith may lawfully waive such rights and benefits pertaining to the subject matter of this general release of claims. Thus, notwithstanding the provisions of section 1542 of the Civil Code of the State of California, and for the purpose of implementing a full and complete release and discharge of all claims, Smith expressly agrees that

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this general release also includes in its effect, without limitation, all claims that Smith does not know or suspect to exist in his favor at the time of execution hereof, and that this general release extinguishes any and all such claims.

7. No Admission of Liability. By entering into this Agreement, the Company does not suggest or admit to any liability to Smith or that it or anyone else violated any law or any duty or obligation to Smith.

8. No Disparagement. Neither party will make any negative, disparaging, detrimental or derogatory comments to any third party concerning the other party, or, with respect to the Company, concerning any of its current and former officers, directors, shareholders, employees, representatives, attorneys and agents, as well as its predecessors, parents, subsidiaries, affiliates, divisions, and successors in interest.

9. Confidentiality. Smith agrees that he will not disclose to any person or otherwise use any proprietary or confidential information, including trade secrets, customer lists, processes, records of research, proposals, reports, methods, processes, techniques, computer software or programming, or budgets or other financial information, regarding the Company, its business, properties, customers or affairs (“Confidential Information”) obtained by Smith at any time during his employment by the Company. Smith may use and disclose Confidential Information to the extent necessary to assert any right or defend against any claim arising under this Agreement if necessary to comply with any law or valid legal process. Smith agrees that he has not removed any documents, records or other information from the premises of the Company containing any such Confidential Information and acknowledges that such documents, records and other information are the exclusive property of the Company.

In addition, Smith agrees that he will not disclose any of the terms of this Agreement to anyone other than his immediate family or legal counsel, except as such disclosure may be required for accounting or tax reporting purposes or as otherwise may be required by law.

10. No Solicitation of Employees. Smith agrees that for the 30-month period following the Retirement Date, he will not, nor will he encourage others to, directly or indirectly, solicit, recruit, or encourage any current employees of the Company or any of its subsidiaries for employment with another bank, financial institution or insurance brokerage company or any other entity engaged in a business or activity that is comparable to or competitive with any business or activity of the Company or any of its subsidiaries. If the Company has a good faith belief that Smith has violated the terms of this section, it will immediately cease making any payments under the terms of this Agreement. Both parties retain the right to seek a determination on any such claimed breach pursuant to Section 12 below.

11. No Solicitation of Customers. Smith also agrees that for the 30-month period following the Retirement Date, he will not, nor will he encourage others to, directly or indirectly, solicit, recruit, or encourage any current customers or clients of the Company or any of its subsidiaries to cease doing business with the Company or any of its subsidiaries or to do business with any other bank, financial institution or insurance brokerage company or any other entity engaged in a business or activity that is comparable to or competitive with any business or activity of the Company or any of its subsidiaries. If the Company has a good faith belief that Smith has violated the terms of this section, it will immediately cease making payments under

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the terms of this Agreement. Both parties retain the right to seek a determination on any such claimed breach pursuant to Section 12 below.

12. Arbitration. The parties agree that any and all disputes, controversies or claims of any kind or nature arising out of or relating to this Agreement or the breach or interpretation thereof, including but not limited to any arising out of or in any way related to Smith’s employment with the Company or the termination thereof, shall be submitted to binding arbitration under the auspices and rules of Judicial Arbitration and Mediation Services, Inc. (“JAMS”) in Santa Clara County, California. In the event that JAMS is unable or unwilling to conduct any such arbitration or has discontinued its business, the parties agree that any and all such disputes, controversies or claims shall be submitted to binding arbitration under the auspices and rules of the American Arbitration Association (“AAA”) in Santa Clara County, California. Included within this provision are any claims alleging fraud in the inducement of this Agreement, or relating to the general validity or enforceability of this Agreement, or claims based on a violation of any local, state or federal law, such as claims for discrimination or civil rights violations under Title VII of the Civil Rights Act of 1964, the California Fair Employment and Housing Act, the Age Discrimination in Employment Act and the Americans with Disabilities Act. Notice of the demand for arbitration shall be filed in writing with the other party to this Agreement and with JAMS (or AAA, if applicable). In no event shall the demand for arbitration be made after the date when institution of legal or equitable proceedings based on such claim, dispute or other matter in question would be barred by the applicable statute of limitations. The arbitration shall be subject to commercial rules and procedures used or established by JAMS (or AAA, if applicable). Notwithstanding anything to the contrary in the JAMS (or AAA, if applicable) rules and procedures, the arbitration shall provide for (i) written discovery and depositions adequate to give the parties access to documents and witnesses that are essential to the dispute and (ii) a written decision by the arbitrator that includes the essential findings and conclusions upon which the decision is based. Subject to Section 13 below, the parties shall bear their own costs and attorneys’ fees incurred in conducting the arbitration, and shall split equally the fees and administrative costs charged by the arbitrator and JAMS (or AAA, if applicable) unless required otherwise by applicable law. Any award rendered by the arbitrator shall be final and binding upon the parties, and as applicable, their respective heirs, beneficiaries, legal representatives, agents, successors and assigns, and may be entered in any court having jurisdiction thereof. Any arbitration hereunder shall be conducted in Palo Alto, California, unless otherwise agreed to by the parties.

13. Attorneys Fees. In the event of any arbitration or litigation concerning any controversy, claim or dispute between the parties hereto, arising out of or relating to this Agreement or the breach hereof, or the interpretation hereof, the prevailing party shall be entitled to recover from the non-prevailing party reasonable expenses, attorneys’ fees and costs incurred in connection therewith or in the enforcement or collection of any judgment or award rendered therein. The “prevailing party” means the party determined by the arbitrator(s) or court, as the case may be, to have most nearly prevailed, even if such party did not prevail in all matters, not necessarily the one in whose favor a judgment is rendered.

14. Successors. This Agreement shall be binding upon and shall inure to the benefit of the parties hereto and their respective successors and assigns; provided, however, that Smith may not assign any interest in this Agreement without the prior written consent of the Company.

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15. Entire Agreement. This Agreement constitutes the full, complete and final expression of the parties’ agreement on the subject hereof, and supersedes all prior negotiations and agreements on such subject, whether written or oral. This Agreement may not be modified, altered or amended, either expressly or impliedly, unless in writing signed both by Smith and by the Company’s Chief Executive Officer.

16. Severability. Should any provision of this Agreement for any reason be declared invalid, void or unenforceable by an arbitrator or court of competent jurisdiction, the validity and binding effect of any remaining portions of this Agreement shall remain in full force and effect as if this Agreement had been executed with such invalid, void or unenforceable provisions eliminated; provided, however, that the remaining provisions still reflect the intent of the parties.

17. Applicable Law. This Agreement shall be governed by and interpreted in accordance with the laws of the State of California, without giving effect to conflict of law provisions.

18. Joint Participation in Preparation of Agreement. The parties hereto participated jointly in the negotiation and preparation of this Agreement, and each party has had the opportunity to obtain the advice of legal counsel and to review, comment upon, and redraft this Agreement. Accordingly, it is agreed that no rule of construction shall apply against any party or in favor of any party. This Agreement and each of its provisions shall be construed as jointly prepared by the parties, and any uncertainty or ambiguity shall not be interpreted against any one party and in favor of the other.

SMITH UNDERSTANDS THAT HE MAY CONSULT WITH AN ATTORNEY PRIOR TO SIGNING THIS AGREEMENT AND THAT HE IS GIVING UP ANY LEGAL CLAIMS, BOTH KNOWN AND UNKNOWN, HE HAS AGAINST THE COMPANY. BY SIGNING THIS AGREEMENT SMITH ACKNOWLEDGES THAT HE DOES SO KNOWINGLY, WILLINGLY AND VOLUNTARILY IN EXCHANGE FOR THE COMPANY’S PAYMENTS AND OBLIGATIONS UNDER THIS AGREEMENT AND UNDER THE CONSULTING AGREEMENT.

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