There are various synonyms that can be used for the phrase "pressed one's hand". Some of the common substitutes include shaking hands, grasping one's hand, clasping hands, gripping firmly, and squeezing tightly. These phrases are typically used to describe a gesture of greeting or affection between two people. Depending on the context, other related phrases like holding hands or patting someone on the back may also be used as synonyms. Overall, these phrases convey a sense of warmth and human connection, and can be used in a range of different situations, from professional introductions to emotional reunions between friends or family members.