Exhibit 99.1

Certification

Pursuant to the requirement set forth in Section 906 of the Corporate Fraud Accountability Act of 2002, David L. Kalkbrenner and Steven C. Smith each hereby certify as follows:

1.    They are the duly appointed Chief Executive Officer and Chief Financial Officer, respectively, of Greater Bay Bancorp, a California corporation (the “Company”).

2.    Based on their knowledge, the Company’s annual Report on Form 10-K for the year ended December 31, 2002, and to which this Certification is attached as Exhibit 99.1 (the “Periodic Report”), fully complies with the requirements of section 13(a) or section 15(d) of the Securities Exchange Act of 1934 and the information contained in the Periodic Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

IN WITNESS WHEREOF, the undersigned have set their hands hereto as of this 4th day of March, 2003.

/s/    DAVID L. KALKBRENNER        

DAVID L. KALKBRENNER

CHIEF EXECUTIVE OFFICER

/s/    STEVEN C. SMITH         

STEVEN C. SMITH

CHIEF FINANCIAL OFFICER