UPDATE - 1/27@2:47PM: It should also be noted that TOOL drummer Danny Carey thanked Peart in his acceptance speech for the band's Best Metal Performance Grammy win (for their song 7empest) as seen in this video.
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As expected, Neil Peart was mentioned during the In Memoriam segment of last night's Grammy Awards ceremony. A very short video snippet of Peart in concert was shown with the caption NEIL PEART - drummer, lyricist Rush. You can watch video of the In Memoriam below or at this location (at about the 19-second mark). Canada's Grammy equivalent - the JUNO Awards - will take place in March and we should expect a more significant recognition of Peart during that ceremony given that he was from Canada and Anthem/SRO's Pegi Cecconi will be receiving the 2020 Walt Grealis Special Achievement Award - not to mention Rush's large collection of JUNO Awards. So it's possible that some sort of special tribute (speeches and/or performances?) will occur, but nothing's been confirmed as of yet. This year's Rock Hall induction ceremony will take place in Cleveland on May 2nd, and that ceremony should also at least include a mention of Peart in the In Memoriam segment, but there's also an outside possibility that they'll put together some kind of tribute performance to open the show. Past ceremonies have included musical tributes to recently-deceased inductees such as David Bowie and Prince, so there is precedence. However, given the Rock Hall's past history with Rush and progressive rock in general, I wouldn't bet on it.