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                                                                   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 report on Form 10-Q/A for Medwave, Inc. (the
    "Registrant");

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 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
             my 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:    February 14, 2005



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


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