There may come a time, especially in "city" games where the whole game takes place in one set locale, when you want to confront your players with someone on the next power level up. Maybe they're making too much of a mess and the NPCs want them to quiet down, maybe they're about to cross over into this power level and people are taking notice, or maybe the big bad NPC just wants to kick around a few PCs. The reason doesn't matter, but how you handle it does. So, let's talk about that.
Have A Goal In Mind
The first thing you want to do is have a goal in mind. This goal shouldn't be "kill all the PCs" because then you're just wiping your game with someone they have no chance against. That's a bad thing, if you don't remember. However, having another goal in mind can be a great way to do it. This way, the NPC can be all mean and powerful, the PCs can survive, and they may even feel like they also accomplished something. Course, the PCs feeling accomplished and not like they just got their ass kicked is entirely up to the goal, and may not be something you actually want them to feel.
Make It Quick
This may seem counter productive, but make it quick. Use the NPCs tricks quickly, and put the PCs out of the fight quickly. Remember what I said about not killing, but that doesn't mean you can't knock out. There are a few reasons you want to make it quick but chief among them is this: the faster it happens, the more impact it will have. Who are you more scared of? The guy that slowly widdled you down over thirty combat rounds? Or the guy that casually dropped you in round 2? Also, the other problem with drawing it out is...
Don't Aim At Things...
In any combat heavy game, I treat my PCs the same way I treat a loaded gun. I don't put anything in front of them that I'm not willing to see destroyed. No matter what it is, your PCs will find a way to kill it. Trust me on this one. Most PCs will never surrender, even as the player themselves is bitching about an unwinnable situation. They just keep on throwing those combat dice. For this reason, if you put your big bad NPC in front of a PC, be prepared for that NPC to die. I don't care how much more powerful the NPC is on paper. Unless you are willing to shield it with plot, there is a chance - and probably a larger one than you realize - that the dice are going to let the PC mop the floor with that NPC. The more dice you let his the table, the more likely this is going to happen.
Use it Sparingly
Let's be honest. What you're doing with this is kicking your players' asses to give their characters a wake up call. This isn't going to feel good in the moment to the players, and if it keeps happening it is going to piss them off. So use this sparingly, and warn your players when it is going to come up. You don't have to go into details, just a "some of the people coming after you guys are terrifying. Bring your thinking caps." and you can be good to go.
This is also why you don't want to kill PCs with the intro fight. In the first meeting, the NPCs power is going to be unknown, and anyone who dies is likely going to feel cheated unless they deliberately provoked the fight themselves. Even then, they may feel cheated. A sound thrashing and leaving the person unconscious can get the message across a lot clearer - especially since it also means the PC wasn't enough of a threat to kill.
I'm saying this again here, use these guys sparingly. The higher above your PCs the NPC is, the more sparingly you want to use it. These can be a great way to show "there is more to this city than you thought," but it can also be a great way to make your players think you are just trying to be a dick. So, use it sparingly, ok?
Overall, using an over powering NPC can be a lot of fun. It may be tempting to make it slow and let it linger, but that way leads to disaster as often as not. Keeping it quick makes it like ripping off a bandaid. Sure it stings, but it fades quicker. If you do it slowly, and the PCs don't kill the NPC, then they just spend longer sitting at the table and feeling completely powerless. Not a fun thing at all.
Have you done this before? How did it go? Did your players like it?
In one of my super games, I had an NPC that the PCs named 'Tank Man.' Tank Man had a damage rating, and toughness rating, that was nearly double the highest PC in the group. He was simply impossible for the players to hurt with conventional means, and hurt a lot when he hit people. I even warned the players that they'd need to use their heads when fighting him. Because of that warning, the group didn't feel as bad when their attacks bounced off Tank Man, and what could have been a very annoying encounter ended up being a lot of fun...every time he showed up.