EXHIBIT 32.1

                            CERTIFICATION PURSUANT TO
                             18 U.S.C. SECTION 1350,
                             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, 2005 as filed with the  Securities  and
Exchange Commission on the date hereof (the "Report"),  each of the undersigned,
in the capacities and on the date indicated below, hereby certifies, pursuant to
18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley
Act of 2002, that to his knowledge:

(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.



Date: May 5, 2006

/s/ Gabriel B. Vegh
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Gabriel B. Vegh
Chairman, Chief Executive Officer, and Acting Chief Financial Officer