The Collaborative International Dictionary of English v.0.48:

Compliment \Com"pli*ment\, v. t.
   To praise, flatter, or gratify, by expressions of
   approbation, respect, or congratulation; to make or pay a
   compliment to.
   [1913 Webster]

         Monarchs should their inward soul disguise; . . .
         Should compliment their foes and shun their friends.
                                                  --Prior.
   [1913 Webster]

   Syn: To praise; flatter; adulate; commend.
        [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Compliment \Com"pli*ment\, v. i.
   To pass compliments; to use conventional expressions of
   respect.
   [1913 Webster]

         I make the interlocutors, upon occasion, compliment
         with one another.                        --Boyle.
   [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Compliment \Com"pli*ment\, n. [F. compliment. It complimento,
   fr. comlire to compliment, finish, suit, fr. L. complere to
   fill up. See Complete, and cf. Complement.]
   An expression, by word or act, of approbation, regard,
   confidence, civility, or admiration; a flattering speech or
   attention; a ceremonious greeting; as, to send one's
   compliments to a friend.
   [1913 Webster]

         Tedious waste of time, to sit and hear
         So many hollow compliments and lies.     --Milton.
   [1913 Webster]

         Many a compliment politely penned.       --Cowper.
   [1913 Webster]

   To make one a compliment, to show one respect; to praise
      one in a flattering way. --Locke.

   To make one's compliments to, to offer formal courtesies
      to.

   To stand on compliment, to treat with ceremony.

   Syn: See Adulation.
        [1913 Webster]

WordNet (r) 3.0 (2006):

compliment
    n 1: a remark (or act) expressing praise and admiration
    v 1: say something to someone that expresses praise; "He
         complimented her on her last physics paper" [syn:
         compliment, congratulate]
    2: express respect or esteem for

Moby Thesaurus II by Grady Ward, 1.0:

85 Moby Thesaurus words for "compliment":
   TL, acclaim, accolade, adulate, adulation, applaud, benevolence,
   beslobber, beslubber, best wishes, blandish, blandishment, blarney,
   bless, blessing, blessings, boon, bouquet, bunkum, cajole,
   cajolement, cajolery, commend, commendation, compliments, conceit,
   congratulate, congratulation, congratulations, encomium, eulogy,
   eyewash, fair words, favor, fawn upon, fawning, felicitate,
   felicitation, flatter, flattering remark, flattery, give a bouquet,
   good wishes, gratulate, gratulation, grease, greetings, hail,
   hand it to, homage, honeyed phrases, honeyed words, honor, incense,
   largess, laud, laudation, make fair weather, oil, oil the tongue,
   orchids, palaver, pay a compliment, polite commendation, posy,
   praise, present, pretty lies, recommend, regards, rejoice with,
   respects, salutations, slobber over, soap, soft soap,
   sweet nothings, sweet talk, sweet words, sycophancy, take off,
   trade-last, tribute, wheedle, wheedling