The duke was most complimentary about my sculpture.
2 free, gratis, on the house:
The shoehorn is complimentary when you buy a pair of shoes.
Advanced English Dictionary
+adjective 1 given free of charge: complimentary tickets for the show 2 ~ (about sth) expressing admiration, praise, etc: a complimentary remark + She was extremely complimentary about his work. Compare: UNCOMPLIMENTARY - COMPLIMENT
Collocation Dictionary adj
extremely, highly, very
She made some highly complimentary remarks about their school.
Random quote: Look back over the past, with its changing empires that rose and fell, and you can foresee the future, too.: Marcus Aurelius