| Year | Event | Category | Film | Result |
|---|---|---|---|---|
| 2010 | Cannes Film Festival | Best Actress | (2010) | Winner |
| 2001 | Screen Actors Guild Awards | Outstanding Performance by a Male Actor in a Leading Role | (2000) | Nominated |
| 2001 | British Academy Film Awards | Best Leading Actress | (2000) | Nominated |
| 2001 | Academy Awards | Best Actress | (2000) | Nominated |
| 1997 | Berlin International Film Festival | Silver Bear - Best Leading Performance | - | Winner |
| 1997 | Academy Awards | Best Supporting Actress | (1996) | Winner |
| 1997 | Screen Actors Guild Awards | Outstanding Performance by a Male Actor in a Leading Role | (1996) | Nominated |
| 1997 | Screen Actors Guild Awards | Outstanding Performance by a Female Actor in a Supporting Role | (1996) | Nominated |
| 1996 | Golden Globe Awards | Best Supporting Actress | (1996) | Nominated |
| 1993 | Venice Film Festival | Volpi Cup - Best Actress | - | Winner |
| 1993 | Golden Globe Awards | Best Actress - Drama | Three Colours: Blue | Nominated |