Exhibit 31.1
 CERTIFICATION BY CHIEF EXECUTIVE OFFICER
 I, Frank J. Bramanti, certify that:
 1.
    
    I have reviewed this annual report on Form 10-K of HCC Insurance Holdings, 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 in order 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 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)) 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.
    
    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 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 registrants board of directors (or persons performing 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.
 March
2, 2009
    
    /s/ Frank J. BramantiDate
    
    Frank J. Bramanti, Chief Executive Officer