Source : Webster's Revised Unabridged Dictionary (1913)

Secureness \Se*cure"ness\, n.
   The condition or quality of being secure; exemption from
   fear; want of vigilance; security.

Source : WordNet®

secureness
     n 1: the state of freedom from fear or danger [ant: {insecureness}]
     2: the quality of being fixed in place [syn: {fastness}, {fixedness},
         {fixity}, {fixture}]