The phrase "sigh for" is often used to express a deep longing or yearning for something. There are a number of synonyms that can be used instead of "sigh for" to convey similar meanings. Depending on the context and the type of longing being described, alternatives could include "craving," "aching," "pining," "yearning," "desiring," "longing," "hankering," "wishing," or "coveting." Each of these words carries a slightly different nuance, and choosing the right one can help to more precisely convey the exact type of longing being felt by the speaker or writer.