The phrase "wait up for" means to stay awake until someone arrives or to delay leaving until someone catches up. Some synonyms for this expression include "linger for," "stay up for," "hold out for," "expectant of," and "anticipating." Other related phrases include "keep an eye out for," "wait for," "await," and "watch for." These phrases are commonly used when waiting for someone or something, and they all convey a similar meaning that suggests patience, anticipation, and expectation. Overall, there are many ways to express the concept of waiting up for someone or something, all of which convey a sense of eager anticipation.