Glenn Close won the Tony Awards for Best Leading Actress in a Play twice (1984, 1992). Glenn Close won the Primetime Emmy Awards for Outstanding Lead Actress in a Drama Series twice (2008, 2009). Glenn Close has won contests in 2 domains.
| Year | Contest | Category | For | Sources |
|---|---|---|---|---|
| 2009 | Primetime Emmy Awards | Outstanding Lead Actress in a Drama Series | Damages | 1 · 2 |
| 2008 | Primetime Emmy Awards | Outstanding Lead Actress in a Drama Series | Damages | 1 · 2 |
| 1992 | Tony Awards | Best Leading Actress in a Play | 1 · 2 | |
| 1984 | Tony Awards | Best Leading Actress in a Play | 1 · 2 |