Academy of Motion Picture Arts and Sciences
| Won |
Best Dramatic Score Titanic |
1997 |
| Nominated |
Best Original Dramatic Score Apollo 13 |
1995 |
| Nominated |
Best Original Dramatic Score Braveheart |
1995 |
| Nominated |
Best Original Score Avatar |
2009 |
| Nominated |
Best Score House of Sand and Fog |
2003 |
| Nominated |
Best Score A Beautiful Mind |
2001 |
| Nominated |
Best Score Field of Dreams |
1989 |
| Nominated |
Best Score Aliens |
1986 |
| Won |
Best Song Titanic |
1997 |
| Nominated |
Best Song An American Tail |
1986 |
British Academy of Film and Television Arts
| Nominated |
Best Music Avatar |
2009 |
Broadcast Film Critics Association
| Nominated |
Best Score The New World |
2005 |
Chicago Film Critics Association
| Won |
Best Original Score Titanic |
1997 |
Hollywood Foreign Press Association
| Nominated |
Best Original Score Avatar |
2009 |
| Won |
Best Original Score Titanic |
1997 |
| Nominated |
Best Original Score Braveheart |
1995 |
| Nominated |
Best Original Score Legends of the Fall |
1994 |
| Nominated |
Best Original Score Glory |
1989 |
| Nominated |
Best Original Song Avatar |
2009 |
| Won |
Best Original Song Titanic |
1997 |
Los Angeles Film Critics Association
| Won |
Best Music Score 48 Hrs. |
1982 |
Online Film Critics Association
| Nominated |
Best Score The New World |
2005 |
