Cardima (CADMQ) 10-Q 2005 Q1 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 March 31, 2005 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

Chairman of the Board and Chief Executive Officer

May 11, 2005