Depends upon what court the action originates in. If a trademark case is brought in state court, a state court of appeals would hear the appeal. If a copyright license case is in state court, same rule. If a copyright or trademark case is in federal court, then a federal circuit court of appeals would hear it.
If it is a case of a trademark registration appeal, it would be taken to the Trademark Trials and Appeals Board and could end up in the Court of Appeals for the Federal Circuit (CAFC).