The Collaborative International Dictionary of English v.0.48:

Umpirage \Um"pi*rage\ (?; 48), n. [From Umpire.]
   1. The office of an umpire; the power, right, or authority of
      an umpire to decide.
      [1913 Webster]

            The mild umpirage of the federal Union. --E.
                                                  Everett.
      [1913 Webster]

   2. The act of umpiring; arbitrament. --Bp. Hall.
      [1913 Webster]

WordNet (r) 3.0 (2006):

umpirage
    n 1: mediation by an umpire
    2: the act of umpiring; "the officiating was excellent" [syn:
       umpirage, officiation, officiating, refereeing]

Bouvier's Law Dictionary, Revised 6th Ed (1856):

UMPIRAGE. The decision of an umpire. This word is used for the judgment of
an umpire, as the word award is employed to designate that of arbitrators.