The Collaborative International Dictionary of English v.0.48:

Rightness \Right"ness\, n. [AS. rihtnes.]
   Straightness; as, the rightness of a line. --Bacon.
   [1913 Webster]

   2. The quality or state of being right; right relation.
      [1913 Webster]

            The craving for rightness with God.   --J. C.
                                                  Shairp.
      [1913 Webster]

WordNet (r) 3.0 (2006):

rightness
    n 1: according with conscience or morality [ant: wrongness]
    2: appropriate conduct; doing the right thing [syn:
       appropriateness, rightness] [ant: inappropriateness,
       wrongness]
    3: conformity to fact or truth [syn: correctness, rightness]
       [ant: incorrectness, wrongness]
    4: conformity with some esthetic standard of correctness or
       propriety; "it was performed with justness and beauty" [syn:
       justness, rightness, nicety]

Moby Thesaurus II by Grady Ward, 1.0:

33 Moby Thesaurus words for "rightness":
   absoluteness, accuracy, attention to fact, care for truth,
   correctness, delicacy, exactitude, exactness, faithfulness,
   faultlessness, fidelity, fineness, flawlessness, literalism,
   literality, literalness, mathematical precision, meticulousness,
   niceness, nicety, perfection, preciseness, precision, refinement,
   right, rigidity, rigor, rigorousness, severity, strictness,
   subtlety, textualism, the letter