Gillies and Rittich teamed to backstop the Stockton Heat to the Calder Cup Playoffs last season, combining to start 67 of the team’s 68 regular-season contests.
Gillies, a native of Concord, N.H., went 18-14-4 with a 2.93 goals-against average, a .910 save percentage and one shutout in 2016-17, his first full pro season after being limited to seven appearances the year before. He also made his NHL debut with Calgary, earning a win at Los Angeles on Apr. 6.
Gillies, 23, was a third-round choice by the Flames in the 2012 NHL Entry Draft and played three seasons at Providence College, winning a national championship in 2015.
Rittich, a native of Jihlava, Czech Republic, appeared in 31 games for Stockton last season and went 15-11-4, ranking eighth in the league with a 2.27 GAA, ninth with a .924 save percentage and tied for second with five shutouts.
Rittich, 24, also made his NHL debut with Calgary last season, a relief appearance at San Jose on Apr. 8.