UNC's Chris Rodrigues wrestled in the championship bout of the 125-pound division, but lost to Tom Nato, who wrestled unattached, 8-4.
North Carolina's Evan Sola defeated Jeremy Walsh, also unattached, for a fifth-place finish at 133 pounds, while Jimmy O'Connor also finished fifth after defeating Delaware Val C's Jason Shivak, 8-3, at 165 pounds.
UNC's Mark Canty took third place at 174 pounds with a 4-3 victory against George Mason's P.J. Ross.
The final wrestler to place for the Tar Heels was Ryan Adams, who fell to Penn State's Josh Walker, pinfall 5:08, in the third-place bout.
North Carolina will host the annual Sharpie-Carolina Open next Saturday. The all-day event will be held in Carmichael Auditorium, beginning at 8:30 a.m. The tournament will host American, Cornell, Citadel, Appalachian State, Campbell, Duke and others.