**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 Annual Report on Form 10-KSB of Cardima, Inc. for the year ended
      December 31, 2006;





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 registrant 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 registrant 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 registrant, 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 registrant’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 registrant's internal control over
      financial reporting that occurred during the registrant's most recent fiscal
      quarter (the registrant's fourth fiscal quarter in the case of an annual report)
      that has materially affected, or is reasonably likely to materially affect,
      the
      registrant'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 registrant's auditors and the audit committee of
      registrant'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 registrant'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 registrant's internal control over financial
      reporting.





*Date:
                May 24, 2007*
              
              
              */s/
                Gabriel B. Vegh*
              
              *Gabriel
                B. Vegh*
              *Chairman,
                Chief Executive Officer, and Acting Chief Financial
                Officer*