Schwarz has two children, both student-athletes at the University of Florida. His daughter Taylor plays first base on the Gators' softball team that won the national title in 2015 and was a member of the class of 2016, while his son J.J., born March 28, 1996, in Palm Beach Gardens, Florida, was drafted by the Milwaukee Brewers in the 17th round in 2014, but chose not to sign. He played his first season for the Florida Gators baseball team as a catcher in 2015, and set the single-season program record for home runs by a freshman, with 18.

He played during two seasons at the major league level for the Chicago White Sox and California Angels. He also played one season in Japan for the Yokohama BayStars. Schwarz was drafted by the Chicago Cubs in the 24th round of the 1982 amateur draft. Schwarz played his first professional season with their Rookie league Gulf Coast Cubs in 1982 and his last with the Atlanta Braves' Triple-A Richmond Braves in 1996.

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