One of the many illusions devised by Jim Henson and his team had Muppet characters seated on stools, with no puppeteer in sight. This visual trick was used at its earliest in The Muppet Movie, where Kermit the Frog is shown on a stool during the opening verse of "The Magic Store."
Of Muppets and Men details how the trick was done:
“When, to sing a duet with Andy Williams, Kermit perched on a stool -- apparently without assistance -- viewers inclined to watch for such things probably suspected some elaborate electronic chicanery. In fact, no such thing was employed. The legs of the stool were bisected by a mirror which faced the camera. The mirror reflected the back of the front legs which, given the symmetry of the structure, created the illusion of a complete stool. Jim was able to crouch behind the mirror and operate Kermit as easily as if he were hidden by a solid brick wall.”