| Year | Event | Category | Film | Result |
|---|---|---|---|---|
| 2018 | British Academy Film Awards | Best Supporting Actress | (2017) | Winner |
| 2018 | Academy Awards | Best Supporting Actress | (2017) | Winner |
| 2012 | Screen Actors Guild Awards | Outstanding Performance by a Cast in a Motion Picture | (2011) | Winner |
| 2008 | Screen Actors Guild Awards | Outstanding Performance by a Cast in a Motion Picture | Hairspray | Nominated |
| 2003 | Screen Actors Guild Awards | Outstanding Performance by a Cast in a Motion Picture | (2002) | Nominated |
| 2003 | Golden Globe Awards | Best Actress - Drama | The West Wing | Nominated |
| 2002 | Golden Globe Awards | Best Actress - Drama | The West Wing | Nominated |
| 2000 | Screen Actors Guild Awards | Outstanding Performance by a Cast in a Motion Picture | (1999) | Winner |