What is "to make one's compliments to"

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.

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

Many a compliment politely penned.
--Cowper.

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.