The Collaborative International Dictionary of English v.0.48:

Highness \High"ness\, n. [AS. he['a]hnes.]
   1. The state of being high; elevation; loftiness.
      [1913 Webster]

   2. A title of honor given to kings, princes, or other persons
      of rank; as, His Royal Highness. --Shak.
      [1913 Webster]

WordNet (r) 3.0 (2006):

Highness
    n 1: (Your Highness or His Highness or Her Highness) title used
         to address a royal person
    2: the quality of being high or lofty [syn: highness,
       loftiness] [ant: lowness]
    3: a high degree (of amount or force etc.); "responsible for the
       highness of the rates"

Moby Thesaurus II by Grady Ward, 1.0:

26 Moby Thesaurus words for "Highness":
   Eminence, Grace, Her Excellency, Her Highness, Her Ladyship,
   Her Majesty, His Lordship, His Majesty, Honor, Imperial Highness,
   Imperial Majesty, Lady, Ladyship, Lord, Lordship, Majesty, My Lady,
   My Lord, Reverence, Royal Highness, Royal Majesty, Serene Highness,
   Worship, Your Lordship, milady, milord