1999
• Emmy (Primetime), Outstanding Lead Actress in a Miniseries or Movie for Life of the Party: The Pamela Harriman Story
• Screen Actors Guild Awards, Outstanding Performance by a Female Actor in a Television Movie or Miniseries for Life of the Party: The Pamela Harriman Story
• Golden Globe, Best Performance by an Actress in a Limited Series or Motion Picture Made for Television for Life of the Party: The Pamela Harriman Story

1994
• Golden Globe, Best Performance by An Actress in a Supporting Role in a Series, Miniseries or Motion Picture Made for Television for Queen

1988
• Golden Globe, Best Performance by an Actress in a Miniseries or Motion Picture Made for Television for The Two Mrs. Grenvilles

1987
• Emmy (Primetime), Outstanding Lead Actress for a Miniseries or Special for The Two Mrs. Grenvilles

1985
• Golden Globe, Best Performance by an Actress in a Miniseries or Motion Picture Made for Television for A Streetcar Named Desire

1984
• Golden Globe, Best Performance by an Actress in a Limited Series or Motion Picture Made for Television for Who Will Love My Children?
• Emmy (Primetime), Outstanding Lead Actress in a Limited Series or Special for A Streetcar Named Desire

1983
• Emmy (Primetime), Outstanding Lead Actress in a Limited Series or Special for Who Will Love My Children?

1978
• Golden Globe, Best Performance By an Actress in a Supporting Role in a Motion Picture for Joseph Andrews

1976
• Academy Award, Actress for Tommy
• Golden Globe, Best Performance By an Actress in a Motion Picture - Musical or Comedy for Tommy

1972
• Academy Award, Actress in a Supporting Role for Carnal Knowledge
• Golden Globe, Best Performance By an Actress in a Supporting Role in a Motion Picture for Carnal Knowledge

1964
• Golden Globe, Actress in a Leading Role - Musical or Comedy for Bye Bye Birdie