I'm fairly certain the Cup resides at the winner's school until the league reclaims it. I've seen it displayed in Mariucci Arena (the old one) before as well as UND.
In 1997, the Sioux led the WCHA most of the way and were awarded the Cup I believe in Denver on a Friday night after clinching at least a tie. The next day, the cup was shipped to Minneapolis in the event of a Gopher win and a Sioux loss, which would make Minnesota co-champions. It happened...and the Gophers skated with the MacNaughton on Saturday night. I believe the Sioux were the #1 seed for the tournament and they enacted revenge several weeks later, winning a 4-3 thriller in OT at the old St Paul Civic Center.
If memory serves me right, UND kept the cup for 1/2 a season and then sent it to Minnesota.