complimentary:
1. paying or containing a compliment; expressing courtesy, respect, admiration, or praise
2. given free as a courtesy
a complimentary ticket
complementary:
1. acting as a complement; completing
2. making up what is lacking in one another
Many plain tiles and complementary borders are also available.
[1] Webster's II New College Dictionary[M]. Houghton Mifflin Harcourt, 2005.
[2] Collins Cobuild. Collins COBUILD advanced learner's English dictionary[M]. Collins Cobuild, 2006.