Synonyms for Preciousness (same or very similar meaning)
WordNet sense 1 (the quality possessed by something with a great price or value):
costliness, dearnessWordNet sense 2 (the positive quality of being precious and beyond value):
invaluableness, pricelessness, valuablenessWordNet sense 3 (the quality of being fastidious or excessively refined):
preciosityFrom the ODE community, based on WordNetadd/edit