"Press one's hand" is a commonly used phrase that refers to the act of grasping and squeezing someone's hand as a gesture of greeting, affection, or support. However, there are various synonyms for this phrase that can add variety and depth to one's vocabulary. Some alternatives include clasping, clutching, gripping, embracing, holding, hugging, and shaking hands. Each of these words connotes a slightly different emotion or intention, which can be useful in different contexts. For example, "clutching" suggests a more urgent, desperate grasp, while "hugging" implies a warmer, more intimate embrace. By incorporating these synonyms into your language, you can better convey your specific intentions and emotions.