The Collaborative International Dictionary of English v.0.48:

Preciousness \Pre"cious*ness\, n.
   The quality or state of being precious; costliness; dearness.
   [1913 Webster]

WordNet (r) 3.0 (2006):

preciousness
    n 1: the quality possessed by something with a great price or
         value [syn: costliness, dearness, preciousness]
    2: the positive quality of being precious and beyond value [syn:
       invaluableness, preciousness, pricelessness,
       valuableness]
    3: the quality of being fastidious or excessively refined [syn:
       preciosity, preciousness]