**EXHIBIT
      31.1**





**CERTIFICATIONS**





I,
      Gabriel B. Vegh, Chairman, President, Chief Executive Officer, and Acting Chief
      Financial Officer of Cardima, Inc., certify that:





1.
      I have
      reviewed this Quarterly Report on Form 10-QSB of Cardima, Inc. for the quarter
      ending March 31, 2007;





2.
      Based
      on my knowledge, this report does not contain any untrue statement of a material
      fact or omit to state a material fact necessary to make the statements made,
      in
      light of the circumstances under which such statements were made, not misleading
      with respect to the period covered by this report;





3.
      Based
      on my knowledge, the financial statements, and other financial information
      included in this report, fairly present in all material respects the financial
      condition, results of operations and cash flows of the small business issuer
      as
      of, and for, the periods presented in this report;





4.
      I am
      responsible for establishing and maintaining disclosure controls and procedures
      (as defined in Exchange Act Rules 13a-15(e) and 15d-15(e)) and internal control
      over financial reporting (as defined in Exchange Act Rules 13a-15(f) and
      15d-15(f)) for the small business issuer and have:





a)
      designed such disclosure controls and procedures, or caused such disclosure
      controls and procedures to be designed under our supervision, to ensure that
      material information relating to the small business issuer, including its
      consolidated subsidiaries, is made known to us by others within those entities,
      particularly during the period in which this report is being prepared;





b)
      evaluated the effectiveness of the small business issuer's disclosure controls
      and procedures and presented in this report our conclusions about the
      effectiveness of the disclosure controls and procedures, as of the end of the
      period covered by this report based on such evaluation; and





c)
      disclosed in this report any changes in the small business issuer's internal
      control over financial reporting that occurred during the small business
      issuer's most recent fiscal quarter (the small business issuer's fourth fiscal
      quarter in the case of an annual report) that has materially affected, or is
      reasonably likely to materially affect, the small business issuer's internal
      control over financial reporting; and





5.
      I have
      disclosed, based on our most recent evaluation of internal control over
      financial reporting, to the small business issuer's auditors and the audit
      committee of small business issuer's board of directors (or persons performing
      the equivalent functions):




a)
      all
      significant deficiencies and material weaknesses in the design or operation
      of
      internal control over financial reporting which are reasonably likely to
      adversely affect the small business issuer's ability to record, process,
      summarize and report financial information; and





b)
      any
      fraud, whether or not material, that involves management or other employees
      who
      have a significant role in the small business issuer's internal control over
      financial reporting.





*Date:
                May 21, 2007*
              
              */s/
                Gabriel B. Vegh*
              *Gabriel
                B. Vegh*
              *Chairman,
                Chief Executive Officer, and Acting Chief Financial
                Officer*