Go a-courting is an old-fashioned phrase that refers to the process of courting someone, or trying to win their affections. The crossword solutions for this phrase are SUE (3 letters) and WOO (3 letters). SUE is a verb meaning to make a legal claim against someone, while WOO is a verb meaning to try to gain someone's love or affection. Therefore, the two words together can be interpreted as making a legal claim in order to win someone's affections.