How do you support your (teen) children through a big disappointment or upset?

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DS has narrowly missed out on something he's worked very hard for. He might have the opportunity to try again, but this is not certain and it will delay things.

He's very upset, but trying to be stoic. This is the first time I can’t just say ‘it’ll be ok'. I’m so upset for him and because he’s upset and I don’t know how to approach it.

Argh.

Allow him to be upset. Show him it's OK to be upset and then together make a plan to either try again or find another route/ destination. Nurture him with love and food and time and show your resilience by being positive and pro active about his future.

As so often the first reply nails it.

Let him be upset, it's ok for him to feel his emotions, he will come to you as and when needed

In my experience
Food
Let them know its ok to be upset
Don't push it, let them talk to you if they want.
Say how sorry you are and how its unfair and that everyone involved is an idiot (depends on whether your child will appreciate this, mine did)

Thank you. I wish he wasn’t being so stoic, but you’re right. He'll talk in time.

I don’t know how to be. Don’t want to be too upset (I am - he was so close), but don’t want to be too ‘it’ll be all right'. He’s worked so, so hard. Sometimes it’s easier to miss by a mile than a millimetre.

I'd buy a little gift like a box of chocolates and tell him I'm proud of how hard he worked and that I'm sorry it didn't work out the way everyone wanted.

I agree. Tell him it's totally understandable and normal to be very upset. And encourage him to be very nice to himself while he's feeling low. I watched both my DC when they had big upsets in their teen years, disappear into the bathroom with bowls of ice cream and their laptops set to their favourite comedians while they had long baths. I was quite proud of them comforting themselves when horrible things happened to them.

The other thing I try to say once the initial upset is over, is that there is almost never just one path to what you most want in life. Usually an opportunity seems ultra important because it is a step towards a bigger goal. Chat about what that is and all the other ways he could reach it and the unconventional ways people have reached it in the past.

Stoic isn't a bad response tbh. No point in going to pieces. I'd try the onwards and upwards approach while providing a listening ear if he needs it, and reiterating that he worked so hard, did his absolute best, and sometimes life is just a bit of a bastard.

I can empathise. My DD was a dancer. Rejection was commonplace but always hurt. I've also got a son who is "very good but not quite good enough" at his sport so have been through similar with him.
I agree with everyone else that it's ok for you both to feel sad and the best thing to do initially is probably actually nothing. Don't try to find solutions immediately, just leave some time to let things settle.
This sort of situation is why I hate the Disneyesque message that our young people are often subjected to - you can be anything you want to be if you try hard enough. But you can't. Real life isn't like that, and the unfortunate consequence of this message is that when disappointment comes it is often accompanied by guilt and self blame. I didn't want it as much as the others, I didn't work hard enough, I didn't make enough sacrifices. Of course that's usually rubbish but it's understandable why young people feel that way. I always tried to stress how proud I was of their effort and that lack of effort was not the issue. Some things are just not meant to be and it isn't anyone's "fault". Also that success or failure in any particular thing does not define them and that they are exactly the same person as they were before they opened the result, they are not suddenly a lesser person. Focus on the benefits of the experience in it's own right. The work will have benefited them even if they haven't reached the aimed for goal. We may not get to the destination we set off for but the experience of the journey is still worthwhile, and the new, as yet unknown destination may well be as good or even better than the one we originally planned.
None of that is for the time immediately after the disappointment. Nobody can take that kind of thing in when they are hurting so much, but in my experience, with time, they can move on and start to see things in a different way. But it's tough. And not just for them, for us as parents too. It's ok for you to be sad and to show it, just be sure your DC understands that you are disappointed for them, not in them.
I hope things look brighter soon.

I meant to reply sooner. This helped an awful lot. Similar, although not quite the same. He’s doing better now the 'shock' is over. I need to get through to him that he is not defined by grades/ winning/ getting there first time, but by the person he is. Also that the path does not need to be in a straight line.

Been there a couple of times with my DS, I try to remind him that at 17 very few things will define his life. Lots of paths lead to the same destination etc.
He is so young that even in five years time 'now' will be a distant memory!

Is it sport related? For mine, it always has been. As well as all of the things above, we talk about famous sports stars and how they miss out too (eg how is Maguire feeling now or how annoying would it have been to be a sprinter when Usain Bolt was around or a distance runner when Mo Farah was around), discuss alternatives (is it worth joining a different team for different opportunities or trying a parallel discipline) and how they want to deal with it (storm off in a sulk or go along and support and variations of those).
Also, stoicism isn't bad. Your DS may be acutely aware of the numbers game. He may also have had an inkling for a while that he wasn't going to get selected and that brings its own pressure and heartache.

Please don't do what my parents did to me and be more upset than I was. Also angry too. It made the disappointment for me so much harder. Being positive, giving space to feel the upset, allowing him the space to talk about things when he wants to without getting emotional yourself. Being positive about the future and exploring options together. I really wish mine had been like this.