Is it a complimentary gift or a complementary gift?1
Were you paid a compliment or a complement?2
Do peanut butter and jelly compliment or complement each other?3
To compliment (verb form) is to give “an expression of esteem, respect, affection, or admiration.” A compliment (the noun form) is the expression itself.
To complement (verb form) is to “fill up, complete, or make perfect,” and a complement (the noun form) is the object or person that fills up, completes, or makes perfect.