1. The positive quality of being precious and beyond value
   "The preciousness of her mentor's advice guided her throughout her career";
   - invaluableness, pricelessness, valuableness
    
2. The quality possessed by something with a great price or value
   "The preciousness of the rare gemstone made it a prized possession";
   - costliness, dearness
    
3. The quality of being fastidious or excessively refined
   "The preciousness of his language alienated many readers";
   - preciosity

Type of: affectedness, effeteness, expensiveness, merit, unaffordability, value, worth