Kevin Watt and Thomas McFarlane were arrested after police moved to quell potential disorder between Hibs and Dundee fans before the clash.
Watt is accused of being in possession of a knife and possessing drugs.
McFarlane faces charges of breach of the peace and possessing an offensive weapon.
Watt, 24, of Pilton Park, and McFarlane, 23, of Lanark Road West, Currie, appeared in private on petition at Dundee Sheriff Court yesterday.
Neither man made any plea or declaration.
Sheriff George Way continued both cases for further examination.
Watt was remanded in custody and is expected to appear in court again next week. McFarlane was released on bail.
A heavy police presence was in force around Dens Park, but Tayside Police said the match had passed peacefully.