Merano Cup
Righini debuted for Italy at the 2013 Merano Cup, placing fifth, and then won bronze at the 2013 Golden Spin of Zagreb. After winning the men's title at the 2014 Italian Championships, he took gold at the 2014 Bavarian Open. Righini was selected for the 2014 World Championships in Saitama, Japan. Placing 14th in the short program, he qualified for the free skate, in which he placed 12th, and finished 13th overall.