The song "The Ecstasy Of Gold" is nominated in the Best Rock Instrumental Performance (For solo, duo, group or collaborative performances, without vocals. Includes Rock, Hard Rock and Metal. Singles or Tracks only.) Other nominees are Rush, Joe Satriani, Bruce Springsteen, and Steve Vai.
Here is the complete list of Grammys now owned by Metallica
Best Metal Performance
Year: 2003
Title: St. Anger
Best Rock Instrumental Performance
Year: 2000
Title: The Call Of Ktulu
Best Hard Rock Performance
Year: 1999
Title: Whiskey In The Jar
Best Metal Performance
Year: 1998
Title: Better Than You
Best Metal Performance With Vocal
Year: 1991
Title: Metallica
Best Metal Performance
Year: 1990
Title: Stone Cold Crazy