The Senate voted 37-0 on Tuesday, sending the measure to the House for consideration.
Senate President Robert Stivers, the Manchester Republican who sponsored the measure, said language allowing soldiers to return ballots electronically was stricken because of concerns about hackers. He called for a review of electronic transmission systems before allowing ballots to be returned that way.
Twenty-four other states allow military personnel to return ballots by some form of electronic transmission. Kentucky allows ballots to return only by mail, and that would continue under Stivers' measure.