Best Performance by an Actor in a Supporting Role in a Series, Mini-Series or Motion Picture Made for TV for LA Law (1991) (Nomination).
Best Television Actor in a Drama for NYPD Blue (1996 - Won) (1997, 1999 - Nomination).
Golden Satellite Award
Best Actor in a Television Series for NYPD Blue (1997) (Won).
The episode of NYPD Blue that marked Jimmy's last appearance received this for 'the dignity of the character's exit' (Won).
(Honouring the Best in Hispanic Cinema and Television)
Best Series for The West Wing based on Jimmy's portrayal of a presidential candidate (2006) (Won).
Independent Spirit Awards
Nomination in 1995.
Screen Actors Guild Awards
Outstanding Ensemble Performance in a Drama Series for NYPD Blue (1994 - Won) (1995-1999 - Nomination).
Viewers for Quality Television Awards
Best Supporting Actor in a Drama for LA Law (1990) (Won).