I’m a new dm running my second campaign, and I gave my 2 players (4th level) what I thought would be a fun, easy encounter. Unfortunately the dice were not in their favor, and 4 crits later they’re both dead. I want to continue this campaign but it’s special to their characters. 
I’ve heard that some dms, rather than straight up killing players, will instead give them permanent effects as a trade off for living. I don’t know any of these effects, or where to look, or if it’s homebrew. 
Help?

Is there some way they can credibly have been captured while both "unconscious"? Or did they fail their death saving throws and all that?

You could do it like, an NPC or God they worship resurrected them an x amount of time in game later. But if it's a normal NPC, in doing so they gave up their life to give them one more chance. 

I did that once, but I planned it as part of the story. They woke up several hours later in a dark room with 1 HP and they pretty much immediately took a long rest. I then had their captors put them to work doing manual labor until they escaped. 

 You could speak with your players and simply pretend that this never happened.

GOOD LUCK!

Quote from Nakadnu >>

 You could speak with your players and simply pretend that this never happened.

GOOD LUCK!

Yep, I've done that. Stared at the dice, stared at the players, said, 'Well, that happened. Lets start again and pretend it didn't."

The good old: "it was only a bad dream..." Used that once or twice :-) Not very pretty, but it works.

Many other good suggestions above. Just make sure you talk to your players and explain them this is an exception. Don't let them think you will save them anytime they get in trouble. That takes away some of the danger and fun of the game.

Another tip: Roll behind a screen. That way you could have dropped that final crit... Hopefully both you and your players have "learned" that sometimes when the battle is going bad, the best option is to run! It's OK to remind the players that from time to time, especially when the dice are against them.

You could also give them a brief glimpse of the afterlife. In the forgotten realms, their souls will be send to the Fugue Plane, and if no god collects them and no devil shows interest, they will eventually be judged by Kelemvor.

The Sword Coast Adventurers Guide has some more info, and the forgotten realms wiki has a whole lot more on it.

Maybe a servant of their god shows up and sends them back, because they still have some work to do?

The full death, fails and all unfortunately 

In that case, keep the death. Not because it's better that they died, but because if you undo it now, the players will realize that their life and death aren't determined by the dice and their choices at all—they're determined by you. And that will probably make them even more upset than losing their characters, because they'll feel like, if they can't fail in quests, it's not really them who succeeds. They're just your puppets. (I was actually in a D&D group once that fell apart for almost this exact reason.)

It sucks to lose your campaign, but it's also fun to start over again with a bit more experience! Talk to your players about what new character ideas they have—that usually gets everyone excited.

Lesson learned: When necessary, fudge rolls.

I mean, I know some people hate that, but, the alternative is to by blind luck roll 4 crits and turn an adventure meant to be trivial into a death march.

I've TPKed more than once, but depending on what you were up against, it might well be willing to stabilize and capture the dying PCs (for example, after a nasty Kobold ambush I had the characters stabilized and sold into slavery). There are a lot of ways you can fudge an everyone dies encounter, but it depends a lot on the details. What was the encounter?

Another thing you can do is have an evil cleric in need of minions cast Raise Dead and Geas. Or a custom spell that raises them as undead under the command of the one who raised them.

Keep the death. It will be better that way I promise.

Start up again new characters and all. You can use the same campaign and have the players notice changes to the world created by their former characters. The dead PCs could be famous with a legendary death.

you could reincarnate them, allow them to keep there personality ,   but roll for new race /class,     deem it a  favor from some body   ie a god or  demon  what ever you like   this allows for future  campaign fun   as well as letting them  get use to new skins  but maintain  the characters personality

Thank you everyone for these awesome suggestions! 

Quote from DirkSwiftfists >>

Thank you everyone for these awesome suggestions! 

 No problem  

Here's a suggestion...if your characters had any family, let the player roll up a family member on a quest to find a way to resurrect their dead relative. Then, if the little brothers/whoever succeeds, the original quest can be resumed.

I tell my players that they live "6 seconds at a time", hehe. I always roll attacks and NPC skill checks out front, but not the random encounter dice usually. 

If the players are ok with it, letting them all die and roll up new characters is absolutely the way to go. For the rest of all campaigns with this group, you'll have a free bonus to the tension of all situations - they'll know that it really absolutely is possible for their characters to die.

Build the campaign from there, if you can. Figure out what happens when the PCs die - and roll up a new party to maybe pick up their epic quest where they left off?

If letting the characters die would kill the players' enjoyment of the campaign, then find a way to have them be captured instead, or resurrected, or something. But you should know your audience, if you can.