From Muppet Wiki

A list of appearances that Muppets have made on Emmy Awards and Daytime Emmy Awards broadcasts.

1970

Big Bird joins Dick Cavett as a presenter at the prime-time awards, marking the first appearance of a Sesame Street character at the ceremonies.

1979

Miss Piggy thinks that she and Kermit have been asked to host the show, but he explains that they're just there to read the rules. Piggy is offended: "I did NOT spend six hours with Monsieur Jacques of Encino to read lousy rules!" She pouts while Kermit reads the rules, then refuses to get offstage until she gets a close-up.

2003

Elmo, Zoe, Grover, Rosita, Big Bird and Wayne Brady peform a medley of songs from Mister Rogers' Neighborhood as a tribute to Fred Rogers.

2004

Kermit and Miss Piggy host the pre-show for the Emmys.

2005

Oscar the Grouch and All My Children actor David Canary, both in trash cans, present the award for Outstanding Performer in a Children's Series. Kevin Clash wins the award.

2006

Caroll Spinney is awarded a Lifetime Achievement Award.