The Collaborative International Dictionary of English v.0.48:

Soberness \So"ber*ness\, n.
   The quality or state of being sober.
   [1913 Webster]

WordNet (r) 3.0 (2006):

soberness
    n 1: the state of being sober and not intoxicated by alcohol
         [syn: soberness, sobriety] [ant: drunkenness,
         inebriation, inebriety, insobriety, intoxication,
         tipsiness]
    2: a manner that is serious and solemn [syn: graveness,
       gravity, sobriety, soberness, somberness,
       sombreness]