Muse have been nominated for 3 Grammy Awards

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Rock Performance by a Duo or Group with Vocals
RESISTANCE - Muse

Best Rock Song
RESISTANCE - Matthew Bellamy, songwriter (Muse)

Best Rock Album
THE RESISTANCE - Muse

Congratulations Muse! The winners will be announced on February 13, 2011. A full list of nominees is available here.

Source : http://www.cbs.com/specials/grammys/nominees/