EXHIBIT 23.1
 
               CONSENT OF ERNST & YOUNG LLP, INDEPENDENT AUDITORS
 
   We consent to the reference to our firm under the caption "Experts" in this
Registration Statement and related Prospectus of Cardima, Inc. for the
registration of 8,604,806 shares of its common stock and to the incorporation
by reference therein of our report dated February 3, 1999, with respect to the
financial statements of Cardima, Inc. included in its Annual Report (Form 10-K)
for the year ended December 31, 1998, filed with the Securities and Exchange
Commission.
 
                                          /s/ Ernst & Young LLP
 
Palo Alto, California
March 19, 1999