Peters has received many honorary awards, including a star on the Hollywood Walk of Fame in 1987. She was named the Hasty Pudding Woman of the Year in 1987. Other honors include the Sarah Siddons Award for outstanding performance in a Chicago theatrical production (1994 for "The Goodbye Girl"); the American Theatre Hall of Fame at the Gershwin Theatre in New York City (1996), as the youngest person so honored; The Actors' Fund Artistic Achievement Medal (1999); an Honorary Doctorate from Hofstra University (2002); the Hollywood Bowl Hall of Fame in 2002 and the National Dance Institute 2009 Artistic Honoree. She was the recipient of the Sondheim Award, presented by the Signature Theatre in 2011.