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Exhibit 31.1 Section 302 Certification I, Richard A. Sebastiao, certify that: 1. I have reviewed this annual report of Form 10-K for the year ended December 31, 2004 of Horizon
Offshore, Inc.; 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. 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) Designed such internal control over financial reporting, or caused such internal
control over financial reporting to be designed under our supervision, to provide
reasonable assurance regarding the reliability of financial reporting and the preparation
of financial statements for external purposes in accordance with generally accepted
accounting principles; (c) 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 (d) 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. Date: March 31, 2005 /s/ Richard A. Sebastiao Richard A. Sebastiao
Chief Restructuring Officer
(principal executive officer)
Horizon Offshore, Inc.