A period example

[Uberto (Uberto Renaldi)]

There is actually a period example from 1351 of two claimants to the Duchy of Brittany engaging in a sort of melee tournament to decide who would claim the title of Duke.
Known as The Combat of the Thirty it was "an arranged fight between selected combatants from both sides of the conflict ... among 30 champions, knights, and squires on each side." It was "arranged in the form of an emprise — an arranged pas d'armes ... in the manner of a tournament, with refreshments on hand and a large gathering of spectators."
So, a viable historically accurate method but maybe only useful if there are two contenders for the Crown (perhaps as a result of a lottery or some other method).

P.S. I should point out that this combat was merely one incident in the 24 years long War of the Breton Succession. It had absolutely no affect on the outcome of that war, but "it was considered by contemporaries to be an example of the finest chivalry."

[nathanaeldavranches]

I like this on an emotional level. I feel like there could be a "raising of the banners" where people attend crown and fight for the person they feel will lead them the best. On the other hand, there would probably be an issue with having a very unbalanced field if that were the method used.