Source : Webster's Revised Unabridged Dictionary (1913)

Demureness \De*mure"ness\ (d[-e]*m[=u]r"n[e^]s), n.
   The state of being demure; gravity; the show of gravity or
   modesty.

Source : WordNet®

demureness
     n 1: the trait of behaving with reserve and decorum
     2: the affectation of being demure in a provocative way [syn: {coyness}]