After parts of eight seasons with the Canadiens, Savage was traded to the Phoenix Coyotes on January 25, 2002, along with a 2002 3rd-round pick for Sergei Berezin. On December 27, 2003, he scored the first Coyote goal in Jobing.com Arena. He was soon after traded to the St. Louis Blues for their playoff run. Due to the parameters of the trade, he was claimed off waivers by Phoenix in the off-season.