Outside of works of fiction are there any notable instances of trial by combat?

Yes! There are. Trials by combat are well attested in the historical record.

I hope the other medievalists won't get too upset at me for venturing outside of my narrow field, but its something that I've read up on.

One of the most famous instances of a trial by combat, was also one of the last attested ones, at least in France. In 1386 Jean de Carrouges accused Jacques le Gris of raping his wife Marguerite. Their legal dispute wound its way through the French legal system until the French King Charles VI interceded. Jean de Carrouges had appealed to the king after an unfavorable ruling had been given by a lord he believed to have been sympathetic to Jacques le Gris. In the end it was decided that a trial by combat would be the way that the legal dispute could be resolved. It is of note that this was the culmination in a series of legal decisions that were all based on the original appeals and trial surrounding the original claims.

At the time, if Marguerite's claim was found to be false through a trial, she herself also faced execution. In the trial by combat, if her husband fell she would have been executed as well.

Their legal suit was settled in a trial by combat in the presence of the king and public. In many ways the description of the event was reminiscent of gladiatorial combat, but with numerous differences. The audience on pain of severe punishment was not allowed to vocalize, lest their actions give one contestant an advantage. In addition to this, an effort was made to make both contestants as equal as possible, Jacques le Gris was even knighted to meet his accuser on an even playing field. Each swore on holy relics to righteousness of their cause.

It was clearly an anachronistic approach to justice by this point in Medieval history and was treated as quite a unique happening at the time.

I can't put in all the details of the event, and if you'd like to read up on a late Medieval example of a trial by combat there is The Last Duel:A True Story of Crime, Scandal, and Trial by Combat in Medieval France by Eric Jager which details the lead up to the duel and the duel itself in detail.