I know it's you can catch any Pokemon without fail, but I caught Every legendary/Strong Pokemon with an ultra ball, even thundrus.
note : this is Pokemon black
Give it as he held item for a Pokemon and offer it in a trade. You can end up getting some decent Pokemon this way, one with good IVs perhaps.
There's not really much you can do with it. Same situation happened to me. What did I do? I threw my Master Ball to catch a Patrat.
Basically, keep it as a collectable item, or waste it like I did.
Master Ball can be handy for example if you encounter very weak Shiny pokemon on the wild but you don't have a pokemon that can weaken it before capturing it or you don't have any pokemon with false swipe that time, your only choice that time is to spam pokeballs, a shiny Basculin came out while I'm EV training for speed i have no choice but to spam Ultra Balls luckily i have spare net balls that time. So if it happens you ran out of other balls to catch the shiny maybe you can use Master Ball for it.
Well, if you haven't caught all the legendary pokemon in the game either use it on that or if there is a shiny pokemon that's either gonna destroy your team or got something on it like burn or poison,just use the master ball on that.