The Collaborative International Dictionary of English v.0.48:

Appropriateness \Ap*pro"pri*ate*ness\, n.
   The state or quality of being appropriate; peculiar fitness.
   --Froude.
   [1913 Webster]

WordNet (r) 3.0 (2006):

appropriateness
    n 1: appropriate conduct; doing the right thing [syn:
         appropriateness, rightness] [ant: inappropriateness,
         wrongness]
    2: the quality of being specially suitable [ant:
       inappropriateness, unworthiness]

Moby Thesaurus II by Grady Ward, 1.0:

30 Moby Thesaurus words for "appropriateness":
   account, advantage, aid, allotment, allowance, applicability,
   appositeness, appropriation, aptness, assistance, expediency,
   fitness, grant, grant-in-aid, help, meetness, order, propriety,
   relevance, rightness, service, serviceability, stipend, subsidy,
   subvention, suitability, suitableness, use, usefulness, utility