| Year | Category | Movie | Win/Nominated |
|---|---|---|---|
| 2003 | Best Score | House of Sand and Fog (2003) | Nominated |
| 2001 | Best Score | A Beautiful Mind (2001) | Nominated |
| 1997 | Best Dramatic Score | Titanic (1997) | Win |
| 1997 | Best Song | Titanic (1997) | Win |
| 1995 | Best Original Dramatic Score | Apollo 13 (1995) | Nominated |
| 1995 | Best Original Dramatic Score | Braveheart (1995) | Nominated |
| 1989 | Best Score | Field of Dreams (1989) | Nominated |
| 1986 | Best Score | Aliens (1986) | Nominated |
| 1986 | Best Song | American Tail (1986) | Nominated |
| Year | Category | Movie | Win/Nominated |
|---|---|---|---|
| 2005 | Best Score | New World (2005) | Nominated |
| Year | Category | Movie | Win/Nominated |
|---|---|---|---|
| 1997 | Best Original Score | Titanic (1997) | Win |
| Year | Category | Movie | Win/Nominated |
|---|---|---|---|
| 1997 | Best Original Score | Titanic (1997) | Win |
| 1997 | Best Original Song | Titanic (1997) | Win |
| 1995 | Best Original Score | Braveheart (1995) | Nominated |
| 1994 | Best Original Score | Legends of the Fall (1994) | Nominated |
| 1989 | Best Original Score | Glory (1989) | Nominated |
| Year | Category | Movie | Win/Nominated |
|---|---|---|---|
| 1982 | Best Music Score | 48 HRS. (1982) | Win |
| Year | Category | Movie | Win/Nominated |
|---|---|---|---|
| 2005 | Best Score | New World (2005) | Nominated |