Depending on the severity and cause of the meltdown, my counterpoint might be familiar music, driving in my car (alone, on deserted country roads, radio off), or watching familiar, friendly episodes of shows I like.
If I'm really bad and inconsolable, the only thing that will help calm me down is TV shows. It has to be Frasier or Friends, Friends is the best. Something I've seen before (I've seen the entire series of Friends over 300 times), something I'm very familiar with, something where the characters only deal with sitcom-y problems.
If I'm in a situation that I HAVE to tolerate, grinding my teeth or staring at a tiny spot on the floor or intentionally focusing REALLY HARD on a familiar stim helps dispel a bit of the tension, but it only works a little and for a short time until I can get away and be alone and take the time I need to 'come down.'
I find that I can minimize meltdowns if I intentionally have them at home. I don't mean that I induce a meltdown. I mean that I can usually feel things building up, sometimes for days, so I get home as fast as I can and once I'm safe at home, I let myself have the meltdown at full strength. I let myself crash and burn for a while and I don't try to stop it. I let it burn itself out, and then I usually am so exhausted I fall asleep for an hour or so, and when I wake up, I feel better (or at least blank). If I have a big meltdown at home, it seems like I can tolerate more before I have another one away from home.
I also find that engaging in my counterpoint activities on a regular basis helps stop meltdowns before they start. I watch either Frasier or Friends every day, usually at least 4 episodes. That little bit of calming helps me start from a better place the next day. If I've been out in a social situation, I HAVE to watch an episode or two when I get home. I can't decompress without it. Being able to constantly go back to my comforting activity helps me to tolerate more outside home before melting down; sometimes I can stop or delay a meltdown just by reminding myself that I can do my comforting activity as soon as I get home.
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You don't need to hide, my friend, for I am just like you.