In June 2003, he was drafted in the 35th round of the Major League Baseball Draft by the Arizona Diamondbacks. During his first minor league season in 2003, he pitched in 24 games in relief for the Missoula Osprey of the Pioneer League, ending the year with 15 saves and a 1.40 ERA. Cremidan was pitching with the Midwest League's South Bend Silver Hawks in 2004 before rejoining the Greece national team in early August for the Olympics. He pitched in four games during the tournament, as Greece failed to medal, finishing in seventh place.
