2021
• British Academy of Film & Television Arts, Leading Actress for Clemency

2014
• Screen Actors Guild Awards, Outstanding Performance by a Cast in a Motion Picture for 12 Years a Slave

2013
• Screen Actors Guild Awards, Outstanding Performance by a Female Actor in a Television Movie or Miniseries for Steel Magnolias
• Emmy (Primetime), Outstanding Supporting Actress in a Miniseries or a Movie for Steel Magnolias

2008
• Emmy (Primetime), Outstanding Supporting Actress in a Miniseries or a Movie for Pictures of Hollis Woods

2006
• Emmy (Primetime), Outstanding Supporting Actress in a Miniseries or a Movie for The Water Is Wide
• Screen Actors Guild Awards, Outstanding Performance by an Ensemble in a Comedy Series for Desperate Housewives
• Emmy (Primetime), Outstanding Supporting Actress in a Comedy Series for Desperate Housewives

2001
• Golden Globe, Best Performance by an Actress in a Limited Series or Motion Picture Made for Television for Holiday Heart

1998
• Screen Actors Guild Awards, Outstanding Performance by a Female Actor in a Television Movie or Miniseries for Miss Evers' Boys
• Golden Globe, Best Performance by an Actress in a Limited Series or Motion Picture Made for Television for Miss Evers' Boys

1997
• Emmy (Primetime), Outstanding Lead Actress for a Miniseries or Special for Miss Evers' Boys

1996
• Emmy (Primetime), Outstanding Supporting Actress for a Miniseries or Special for Gulliver's Travels
• Screen Actors Guild Awards, Outstanding Performance by a Female Actor in a Television Movie or Miniseries for The Piano Lesson
• Screen Actors Guild Awards, Outstanding Performance by a Cast in a Motion Picture for How to Make an American Quilt

1995
• Emmy (Primetime), Outstanding Lead Actress in a Miniseries or Movie for The Piano Lesson

1993
• Golden Globe, Best Performance By an Actress in a Supporting Role in a Motion Picture for Passion Fish

1990
• Emmy (Primetime), Outstanding Lead Actress for a Miniseries or Special for A Mother's Courage: The Mary Thomas Story

1987
• Emmy (Primetime), Outstanding Lead Actress for a Miniseries or Special for Unnatural Causes

1986
• Emmy (Primetime), Outstanding Lead Actress in a Drama Series for St. Elsewhere

1985
• Emmy (Primetime), Outstanding Supporting Actress in a Miniseries or a Movie for Words by Heart

1984
• Academy Award, Actress in a Supporting Role for Cross Creek