The state used discretion in counting write-in votes for Miller's rival, Sen. Lisa Murkowski, in last fall's race. Miller sued, saying a strict reading of election law bars that.
Three courts, including the Alaska Supreme Court, ruled against Miller, though a federal judge said he could understand both sides and said the law is poorly written.
Several state lawmakers have expressed interest in clarifying the law.
Miller, who abandoned his legal fight and conceded Dec. 31, tells The Associated Press that giving the state Division of Elections discretion to determine voter intent "places the integrity of the election in peril."
According to Miller, his campaign raised more than $300,000 for his legal challenges. He tells The Associated Press that should be enough to cover his costs.
Murkowski's campaign has said she raised more than $250,000 for her legal bills. She was sworn in for her second full term earlier this month.