Finding synonyms for the phrase "paying court" could help to broaden your writing vocabulary and make your texts more interesting. Some possible alternatives might include "wooing," "flattering," "fawning over," "currying favor with," or "making advances to." Each of these phrases carries a slightly different connotation, so you may choose a synonym based on the tone you wish to convey. For instance, "wooing" might suggest a more romantic or amorous tone, while "flattering" could imply that the person paying court is using excessive compliments to gain favor. Ultimately, the synonym you choose will depend on the context in which you intend to use it.