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 Quarterly Report on Form 10-Q for the period ended March 31, 2003, 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 7th day of May, 2003.

/s/    DAVID L. KALKBRENNER          

David L. Kalkbrenner

Chief Executive Officer

/s/    STEVEN C. SMITH          

Steven C. Smith

Chief Financial Officer

A signed original of this written statement required by Section 906 has been provided to Greater Bay Bancorp and will be retained by Greater Bay Bancorp and furnished to the Securities and Exchange Commission or its staff upon request.