Swing! has been nominated for several awards, including Outstanding Broadway Musical and Outstanding Choreography at the Outer Critics Circle Awards. Lynne Taylor-Corbett was nominated for Outstanding Choreography, Everett Bradley and Ann Hampton Callaway received Performance nominations at the Theatre World Awards. Additionally, Lynne Taylor-Corbett was nominated for Outstanding Choreography, Swing! was nominated for Outstanding New Musical, and Harold Wheeler was nominated for Outstanding Orchestrations at the Drama Desk Awards.