Before the fight, a skill challenge. Perform (Oratory), (Poetry), and (Comedy). You are basically doing a rap battle to insult your foe. (This was a real thing). Highest combined total gets a morale bonus to attack and damage during combat.

Other possible rules: no outside interference. If you have an animal companion or familiar, they stay out of it.
Attack only your foe. If you're a frenzied berserker and lash out at a spectator, all onlookers are expected to beat you into unconsciousness. You lose the duel.
Weapons: only regular masterwork allowed, no enchantments. They have a selection of any weapon you want to choose from.
Armor and shields: Only regular masterwork, same as weapons.
No sundering. You're fighting your opponent, not the blacksmith.