Perching on' is a phrase used to describe the act of sitting or resting on top of something. It is often used to describe birds that are perched on a branch or other object. The term 'perching on' can also be used to describe people who are sitting on a fence, bench, or other object. The crossword solution for the term 'perching on' is ATOP, which is a four-letter word meaning to be situated on the highest point of something.