Robins has won or been nominated for several awards for her work including the Actors' Equity Foundation Joe A. Callaway Award (1995), for The Merchant of Venice, the 2012 Drama Desk Award, Outstanding Ensemble for Sweet and Sad, the Lucille Lortel Award nominations for Outstanding Featured Actress (2004) for Frozen and Outstanding Lead Actress (2007) for Sore Throats, the 1997 Joseph Jefferson Award Best Actress for A Streetcar Named Desire at The Steppenwolf Theatre, the Helen Hayes Award nomination, 1997 Supporting Performer, Non-Resident Production for Mrs. Klein, and the Drama League Award.