The Collaborative International Dictionary of English v.0.48:
Secureness \Se*cure"ness\, n. The condition or quality of being secure; exemption from fear; want of vigilance; security. [1913 Webster]WordNet (r) 3.0 (2006):
secureness n 1: the state of freedom from fear or danger [ant: insecureness] 2: the quality of being fixed in place as by some firm attachment [syn: fastness, fixedness, fixity, fixture, secureness] [ant: looseness]