In autumn 1992, Kovaříková/Novotný moved to train in the United States, choosing Irina Rodnina as their coach. They took silver at two events, the 1992 Skate America and 1992 Grand Prix International de Paris. Ranked fifth in the short and third in the free, they finished fourth at the 1993 European Championships in Helsinki, Finland. They placed sixth in the short, fourth in the free, and fourth overall at the 1993 World Championships in Prague, Czech Republic.