One form of on-field referee can be seen in Ancient Greek Sport. Specifically, the Hellanodikai (the judges of the Ancient Olympic Games) would observe boxing, wrestling, and the Pankration (as well as all other sports taking place at the olympics.) to observe for signs of surrender. The Hellanodikai would also whip athletes during these events who broke the rules. For example, if an athlete began to gouge the eyes, or bite the opponent, the Hellanodikai would whip the offender during the match.

Sources:

Miller, Stephen G. Ancient Greek Athletics. New Haven: Yale University Press, 2004.

Kyle, Donald G. Sport and Spectacle in the Ancient World. Malden, MA: Blackwell Pub., 2007.