Cardima (CADMQ) 10-K 2004 FY Annual 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 Annual Report of Cardima, Inc. (the “Company”) on Form 10-K for the year ending December 31, 2004 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

March 31, 2005