One addendum I wish to make is that even if the fight is wholly handwaved, it should be "believable" within the context of the world. If the Lord High Knight Commander has been established to be, say, a 15th level fighter, saying he was killed in a barroom brawl by a common drunk should make the players VERY suspicious, and if they track down the drunk, they should find he was a Rogue 10/Assassin 8, or that the Knight was poisoned and the "drunk" was a stooge to throw people off the track, or something. This isn't true just of D&D, but of any game with any sort of "power imbalance". If you want Doctor Armageddon, world-smashing villain, to be dead (or.... IS HE?), saying "He died when the entire (NPC) League Of Legends attacked him in his orbital fortress" should work; saying "He was shot by a rookie cop during a bank hold up", doesn't. (Unless, of course, it's a CLUE!)
You don't need to roll out every round, but you should at least make sure the fight outcome is somewhere in the plausible range. There's "handwaving", and then there's hammering a square NPC peg into a round plot hole.