From The Collaborative International Dictionary of English v.0.48 :
Graveness \Grave"ness\, n.
The quality of being grave.
[1913 Webster]
His sables and his weeds,
Importing health and graveness. --Shak.
[1913 Webster]
From WordNet (r) 3.0 (2006) :
graveness
n 1: a manner that is serious and solemn [syn: graveness,
gravity, sobriety, soberness, somberness,
sombreness]