This invention provides a coating composition for use on a food-contact surface of a container (e.g., a food or beverage can) that includes a polymer having one or more segments of Formula I: —O—Ar—Rn—C(O)—O—R1—O—C(O)—Rn—Ar—O— wherein each Ar is independently a divalent aryl group (i.e., an arylene group) or heteroarylene group; R1 is a divalent organic group; each R is independently a divalent organic group; and n is 0 or 1. Containers comprising the polymer and methods of making such containers are also provided.