A crest referred to the symbol at the top of a coat of arms and was displayed by knights on the side of their helmets. Crest could also refer to the decorative feathers ancient Romans wore on the top of their helmets. Katherina is combining these two senses, sarcastically suggesting that Petruchio’s family crest is a coxcomb, the feathers on a cock’s (rooster’s) head. Because these make a rooster look rather ridiculous, a coxcomb is also the name for a clown’s hat.