At the Atlanta Games in 1996, Sim won his first Olympic title by defeating Aleksandr Pavlov of Belarus in the final. He scored two points with a chest-high roll-through with 42 seconds left in regulation time and then added two more points with another roll in overtime to score a 4-0 victory.
Between Games, Sim moved up to 54kg. In the semifinals of the Sydney Games in 2000, he defeated Kang Yong-Gyun of the Democratic People's Republic of Korea (North Korea) 10-0. At the Opening Ceremony, the North and South Koreans had marched together. In this spirit, before the medal matches, Sim gave advice to Kang about the man he would be facing in the bronze-medal match-Andriy Kalashnikov of Ukraine, while Kang gave Sim a scouting report on his opponent in the gold-medal match-Lázaro Rivas of Cuba. Both Koreans won, with Sim scoring early and often against Rivas and prevailing 8-0.