Exhibit 99.1

CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350

AS ADOPTED PURSUANT TO SECTION 906

OF THE SARBANES-OXLEY ACT OF 2002

I, John T. Chambers, President and Chief Executive Officer of Cisco Systems, Inc. (the “Company”), do hereby certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that, to my knowledge:

• the Quarterly Report on Form 10-Q of the Company for the quarter ended April 26, 2003, as filed with the Securities and Exchange Commission (the “Report”), fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

• the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Date: May 14, 2003

/s/    John T. Chambers

John T. Chambers

President and Chief Executive Officer

(Principal Executive Officer)

*    A signed original of this written statement required by Section 906 has been provided to Cisco Systems, Inc. and will be retained by Cisco Systems, Inc. and furnished to the Securities and Exchange Commission or its staff upon request.