I think the main thing is not to take it personally. I had a job a couple of years ago with a grant-awarding body and used to handle calls from lots of angry and/or upset people who'd had their applications rejected.
When I started, I did used to take it personally and it used to perturb and upset me that people would be so angry at *me*. But I just had to learn to accept that they weren't really angry at me, they were angry at the outcome of their application, the decision makers, the organisation and even government funding cuts and the wider economic climate.
Once you start to detach yourself from it emotionally, it gets easier to deal with.
They're going to want to rant and vent a bit, so try to let that be water off a duck's back. But then try to start controlling the narrative a bit 'Yes, I'm sorry it's bad news and it's not what you wanted to hear, and I'm sorry you're angry and upset, but let's look at the reason for the decision and see if there's a way of addressing those issues in a reapplication?'
So hear them out and sympathise but then try to get them to move forwards, what do they want? What can you do to help?
Not in relation to work but more in a personal capacity, one thing that drives me over the edge is when people start parroting about complaints procedures. No. No, I don't want to file a fucking complaint, I just want you to do your jobs competently/resolve the fucking problem. So I'd say think about the actual underlying problem and how to go about solving that, because that's ultimately what people want. Fobbing people off with complaints procedures is just bullshit because it doesn't really achieve anything, just compounds the frustration and anger.
So that's why - back to work scenarios - if anyone said anything about making a complaint I'd signpost them to the relevant policy and procedures but I wouldn't just brush them off, I'd still try to tackle the problem, 'Yes, here's how to make a complaint, but what I'm also going to for you is xyz (email/speak with a colleague to try to get feedback or set up a meeting) to help resolve the problem.'
I had a couple of particularly difficult calls that could have ended up in messy complaints making allegations of racial or disability discrimination (I don't think there had been, but that was their perception of how/why things had gone wrong), but ultimately the complaints weren't lodged because I hadn't just fobbed them off with the complaints procedure, but had proactively dealt with the underlying issues and got them the assistance they needed/set up meetings/put them in contact with colleagues who could help them.
So try not to take it personally and try to achieve some kind of resolution to the problem. And if you can't solve the problem there and then, tell them what you're going to do and follow through - call them back/send them an email to update them 'I said I'd contact X, they're in a meeting all afternoon/off till Wednesday, but I've left a message and I'll chase it up. And in the meantime here's the link to those guidance notes for grant applications' or 'I've had a chat with colleague X and they're going to email/call you tomorrow'. Keep the communication going and keep it positive.