拍马屁 To pat the horse’s rump. To flatter. Under the shorter form 拍马, the Handian dictionary gives the example: “He never fawns on his superiors.”
溜须拍马 To smooth the beard and pat the horse. The Taiwan Ministry of Education dictionary gives the example: “He fawns on those above him and is stern with those below him.”
戴高帽子 To put a tall hat on someone. To flatter or praise someone. In the Qing novel Flowers in the Mirror, an old man says that he has heard that people in this place love flattery most of all. “The northern saying calls it loving to wear tall hats. Today one, tomorrow another, until the head is covered with tall hats.”