There are several synonyms for the phrase "wet with perspiration," which is commonly used to describe the physical state of being sweaty. Some alternative expressions include "drenched with sweat," "soaked in perspiration," "moist with exertion," "sopping with moisture," and "sweat-soaked." All of these phrases can be used to convey a similar image of a person who has been physically active and is now covered in sweat. Depending on the context of the situation, some of these synonyms may be more appropriate or descriptive than others, but all can be considered useful in conveying the idea of being sweaty.