Saint Mary's University of Minnesota Athletics

Zaremba played in 118 games during his four seasons with the Saint Mary’s baseball team, compiling a .289 batting average—going 86-for-296 with 14 doubles, eight triples and five home runs. He drove in 51 career runs and was walked 40 times.

Zaremba enjoyed his best statistical season in 1978, when he hit .427 (41-for-96), with seven doubles, five triples, and three home runs. He scored 22 runs that junior season. His five triples during his junior season rank No. 2 all-time and his 25 walks as a senior in 1978 rank third, while his eight career triples leave him sitting sixth all-time.