I think a formal duel was an outstanding means of settling a dispute, and could still be today. Its also interesting to note that the ascension and decline of dueling among the nobility/aristocracy was strongly correlated with the weakness of the monarch. When the kings were powerful, it was more customary for them to settle the disputes among their subordinates, but when the kings were weak, the individuals in question solved disputes more or less themselves. There also existed judicial combats, which took the form of a duel, although the king would officiate in some respects. The Jarnac-Chastajuleaux (however its spelled, search “coup de jarnac”) combat is an easily accessible example, where Chastahooligan was defeated by Jarnac, the combat being the result of an insult, and approved by the king.
what I find interesting from a libertarian perspective is the efficiency of the process. Robert and Allen have a dispute. Robert and Allen agree to settle their dispute with violence. They (and other interested parties, all consenting adults) go to a secluded area. They perform combat according to specific rules, which if followed, in the worst case scenario might result in 4 deaths (both principals and both seconds). As likely as not, they would reach a settlement with perhaps one injury, or one death, and the loss of a day. Lawyers and courts cost money, and you already lose a day’s wages, so basically the only advantage you have is that, you are less likely to have a physical confrontation on that day. But people do get assaulted in courthouses, from time to time, and you have to subject yourself to being disarmed and taken by surprise. And you have to pay a bunch of people to show up, and run things according to their preferences rather than your own. We cant say a lot about the different duelling codes that existed in 19th century southern united states, probably because the women of the families burned those books as soon as they could get away with it, but we do know there were several. And so Robert and Allen could choose from a variety of forms of combat, if they wished.