Cardima (CADMQ) 10-Q 2003 Q2 Quarterly report

Exhibit 32.1

CERTIFICATION PURSUANT TO

SECTION 1350 OF CHAPTER 63 OF 18 U.S.C.

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Quarterly Report of Cardima, Inc. (the “Company”) on Form 10-Q for the quarter ending June 30, 2003 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Gabriel B. Vegh, Chief Executive Officer of the Company, certify pursuant to § 1350 of Chapter 63 of 18 U.S.C., as adopted pursuant to § 906 of the Sarbanes-Oxley Act of 2002, that:

(1) The Report fully complies with the requirements of section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

(2) The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

/S/    GABRIEL B. VEGH        

Gabriel B. Vegh

Chief Executive Officer

August 14, 2003

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

This certification accompanies this Report pursuant to Section 906 of the Sarbanes-Oxley Act of 2002 and shall not, except to the extent required by the Sarbanes-Oxley Act of 2002, be deemed filed by the Company for the purposes of Section 18 of the Securities Exchange Act of 1934, as amended.