
<PAGE>
                                                                    EXHIBIT 99.2
 
          THIS PROXY IS SOLICITED ON BEHALF OF THE BOARD OF DIRECTORS
 
    This Proxy will be voted as directed, but if no direction is indicated, it
will be voted FOR the Merger Proposal and in the discretion of the proxies on
such other matters as may properly come before the Special Meeting or any
adjournments or postponements thereof.
 
    Receipt of the Notice of Special Meeting and the attached Proxy
Statement/Prospectus is hereby acknowledged.
 
    Please sign exactly as your name appears on the proxy. Joint owners should
each sign personally. If signing as attorney, executor, administrator, trustee
or guardian, please include your full name. Corporate proxies should be signed
by an authorized officer.
 
<TABLE>
<S>                                            <C>
                                               Dated: , 1998
 
                                                        (Signature of Stockholder)
</TABLE>
 
  PLEASE SIGN, DATE AND RETURN THIS CARD PROMPTLY USING THE ENCLOSED ENVELOPE.
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                                     PROXY
                                ONBANCORP, INC.
                        SPECIAL MEETING OF STOCKHOLDERS
 
    The undersigned hereby appoints David C. Ingles and William M. LeBeau and
each of them, the proxy or proxies of the undersigned, with full power of
substitution, to vote all shares of Common Stock of ONBANCorp, Inc.
("ONBANCorp") which the undersigned is entitled to vote at the Special Meeting
of Stockholders of ONBANCorp to be held on Tuesday, March 17, 1998, at the
Marriott Hotel, 6302 Carrier Parkway, East Syracuse, New York, and at any
adjournments or postponements thereof, with all power which the undersigned
would possess if personally present (i) as designated with respect to the
proposal set forth below and described in the accompanying Joint Proxy
Statement/Prospectus, and (ii) in their discretion with respect to such other
matters as may properly come before the Special Meeting or any adjournments or
postponements thereof.
 
THE BOARD OF DIRECTORS OF ONBANCORP RECOMMENDS A VOTE FOR THE MERGER PROPOSAL.
 
PROPOSAL (the "Merger Proposal") to approve the Agreement and Plan of
Reorganization and the related Agreement and Plan of Merger, each dated as of
October 28, 1997, by and among First Empire State Corporation, ONBANCorp and
Olympia Financial Corp.
 
            / /  FOR            / /  AGAINST            / /  ABSTAIN
