Tvrdon represented with Slovakia at the 2010 IIHF World U18 Championships, where he recorded three goals and one assist in six games. Two years later, he represented Slovakia's national junior team at the 2012 World Junior Ice Hockey Championships, where he recorded three goals and one assist in six games, finishing as the second-leading goal scorer on the team. Slovakia finished sixth in the tournament after losing their quarterfinal and the fifth place consolation match.