| Organizations | Year | Category | Work | Result | Ref. |
| AACTA Awards | 2022 | Best Film | Belfast | Nominated | |
| Best Direction | Nominated | |
| Best Screenplay | Nominated | |
| AARP Movies for Grownups Awards | 2018 | Best Director | Murder on the Orient Express | Nominated | |
| 2019 | All Is True | Nominated | |
| Best Grownup Love Story | Nominated |
| 2022 | Best Movie | Belfast | Won | |
| Best Director | Nominated |
| Best Screenwriter | Nominated |
| Best Intergenerational Film | Nominated |
| Best Time Capsule | Nominated |
| Critics' Choice Movie Awards | 2012 | Best Supporting Actor | My Week with Marilyn | Nominated | |
| 2022 | Best Director | Belfast | Nominated | |
| Best Original Screenplay | Won |
| Broadcasting Press Guild | 2008 | Best Actor | Wallander: One Step Behind | Won | |
| Capri Hollywood Film Festival | 2011 | Best Ensemble Cast | My Week with Marilyn | Won | |
| 2021 | Best Original Screenplay | Belfast | Won | |
| Chicago Film Critics Association | 1989 | Best Actor | Henry V | Nominated | |
| 1996 | Hamlet | Nominated | |
| Detroit Film Critics Society | 2011 | Best Supporting Actor | My Week with Marilyn | Nominated | |
| European Film Awards | 1990 | European Actor of the Year | Henry V | Won | |
| Young European Film of the Year | Won |
| 2022 | European Screenwriter | Belfast | Nominated | |
| Golden Raspberry Awards | 1999 | Worst Supporting Actor | Wild Wild West | Nominated | |
| Independent Spirit Awards | 1993 | Best Film | Much Ado About Nothing | Nominated | |
| London Film Critics' Circle | 1993 | British Producer of the Year | Much Ado About Nothing | Won | |
| 2002 | British Supporting Actor of the Year | Harry Potter and the Chamber of Secrets | Won | |
| 2011 | Supporting Actor of the Year | My Week with Marilyn | Won | |
| Middleburg Film Festival | 2021 | Director Spotlight Award | Lifetime Achievement | Won | |
| Phoenix Film Critics Society | 2011 | Best Supporting Actor | My Week with Marilyn | Nominated | |
| SCAD Savannah Film Festival | 2021 | Lifetime Achievement in Acting and Directing Award | Won | |
| San Diego Film Critics Society | 1996 | Best Actor | Hamlet | Won | |
| Sant Jordi Awards | 1989 | Best Foreign Actor | Henry V | Won | |
| Satellite Awards | 2005 | Best Actor – Miniseries or Television Film | Warm Springs | Nominated | |
| 2009 | Best Actor – Miniseries or Television Film | Wallander: One Step Behind | Nominated | |
| 2011 | Best Supporting Actor – Motion Picture | My Week with Marilyn | Nominated | |
| 2021 | Best Motion Picture – Drama | Belfast | Won | |
| Best Director | Nominated |
| Best Original Screenplay | Won |
| Saturn Awards | 1994 | Best Actor | Frankenstein | Nominated | |
| Vancouver Film Critics Circle | 2011 | Best Supporting Actor | My Week with Marilyn | Nominated | |
| WDCAFC Awards | 2011 | Best Supporting Actor | My Week with Marilyn | Nominated | |
| WhatsOnStage Awards | 2004 | Best Actor in a Play | Edmond | Won | |
| 2009 | Ivanov | Won | |
| 2017 | The Entertainer | Nominated | |
