Exhibit 23.1 CONSENT OF MARC LUMER & COMPANY, INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM We hereby consent to the incorporation by reference in the Registration Statements on Forms S-3 (No. 333-36026, No. 333-64536, No. 333-74753, No. 333-76780, No. 333-100392, No. 333-102837, No. 333-108778, No. 333-104791, No. 333-112165, and No. 333-121876) and Forms S-8 (No. 333-38506, No. 333-32545, No. 333-65916, No. 333-65928, No. 333-102744, No. 333-116328 and No. 333-106922) of Cardima, Inc. of our report dated April 14, 2005, relating to the financial statements, which appear in the Annual Report on Form 10-K for the year ended December 31, 2005. /s/ MARC LUMER & COMPANY San Francisco, California May 4, 2006