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                                                                    EXHIBIT 31.1

              CERTIFICATION OF CHIEF EXECUTIVE OFFICER, PURSUANT TO

                  SECTION 302 OF THE SARBANES-OXLEY ACT OF 2002

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        I, Timothy O'Malley, certify that:

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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.      The Registrant's other certifying officer(s) and I are 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.      The Registrant's other certifying officer(s) and 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.

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Date:   February 17, 2004       By:  /s/ Timothy J. O'Malley
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                                     Timothy J. O'Malley
                                     President and Chief Executive Officer
                                     (Principal Executive Officer and
                                     Principal Financial Officer)