<PAGE>

                                                                    EXHIBIT 31.1

              CERTIFICATION OF CHIEF EXECUTIVE OFFICER, PURSUANT TO
                  SECTION 302 OF THE SARBANES-OXLEY ACT OF 2002


         I, Timothy O'Malley, certify that:

1.   I have reviewed this quarterly report on Form 10-Q for Medwave, Inc. (the
     "Registrant");

2.   Based on my knowledge, this quarterly 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 quarterly report, fairly present in all
     material respects the financial condition and 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)) 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 change 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 the 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 13, 2004


                                       By: /s/ Timothy J. O'Malley
                                           -------------------------------------
                                           Timothy J. O'Malley
                                           President and Chief Executive Officer
                                           (Principal Executive Officer and
                                           Principal Financial Officer)



                                       15