赞美 (zànměi) is a general, warm verb for 'to praise, to admire' — it focuses on expressing approval of someone's qualities or achievements. It's less formal than 赞扬 (zànyáng, more written/formal) and broader than 赞赏 (zànshǎng, which emphasizes appreciation/esteem). 称赞 (chēngzàn) is more about commending someone's actions in speech.