I saw a beauty parlour which invites people in for a complimentary consultation. (It was closed, so I didn’t take them up on it.) This is correct (complementary would be incorrect), but it made me think of the expressing a compliment meaning rather than the given for free meaning. Come in and we will say very nice things about you.
I guess beauty parlour staff walk a fine line in their consultations. If they say too many positive things, the prospective client might decide they don’t need any treatments/products after all, but if they say too many negative things, they might just leave.