It is now up to Miller whether the election is finally over.
The court, in its decision Wednesday, said it found "no remaining issues raised by Miller that prevent this election from being certified."
A federal judge, who had put a hold on certification to give the state courts time to rule on Miller's claims, said he would give Miller 48 hours to plead any outstanding issues to him once the high court had ruled.
Miller did not immediately comment.
The decision follows Miller's appeal of a state judge's decision to toss out his challenge to the state's counting of ballots for Murkowski. Miller maintained that the state should be held to the letter of the law, which calls for write-in ballots to have the oval filled in and the last name of a candidate or the name as it appears on the declaration of candidacy written in.
The state pointed to case law in defending its practice of using discretion in determining voter intent, allowing ballots with misspellings to be counted toward Murkowski's tally.
Murkowski mounted a write-in campaign, the likes of which Alaska had never seen, after losing the primary to Miller. Unofficial results showed her leading by 10,328 votes following a tedious, weeklong handcount of ballots. The lead narrowed to 2,169 votes when ballots challenged by Miller's campaign were excluded.