I often detached myself from my big feelings by intellectualizing them....turning it into "I think" instead of "I feel". It's not a bad way of coping when you need it, if you don't overuse it, but it also leaves those feelings there, thought about but not felt, if that makes sense. So anyway, when I found myself putting aside the intellectualizing and just trying to sit with my feelings, it did feel like I was going to be swamped, like huge waves crashing over me.
I had to sometimes take deep breaths, remind myself "this is just a feeling, just a feeling, I can feel it and be with it and be OK, I have power over it".
It is possible to sit with the bigness of a feeling and not be carried away by it....by not feeding it with panicked, fearful thoughts, for one, I think. Feeling the emotion without feeding it.....
In the practical sense, writing helps me. Sometimes I have a hard time writing my feelings, so I play the piano, or I go run; whatever seems best at the moment.