Following his major triumph, he improved further with skill, strategy, and training to qualify for the World and European Championships; however, he suffered numerous setbacks during the competition by placing farther from the medal podium.

After long years of defeat and struggles in the competition, Švec finally managed to repeat his silver medal at the 2006 World Championships in Guangzhou, China, losing out to Estonia's Heiki Nabi by a technical score of 1–3.

In addition to his numerous achievements at both the World and European championships, Švec was one of two Greco-Roman wrestlers from the Czech Republic, along with David Vála, to compete at three Olympic games.

He lost to Garrett Lowney of the United States, without receiving any technical score, and Russia's Gogi Koguashvili, who previously defeated him at the World Championships two years before.

[2] Having lost in the semi-final round, Švec qualified for the bronze medal bout, but was defeated by Kazakhstan's Asset Mambetov, who earned more points than him in the second period of the match, with a three-point counter takedown, and two-point reverse exposure.