So it's that time again - time to move the tomato plants from the little seedling cells into seedling pots. I'm especially careful when doing this since I only minimally thin the tomatoes - I only remove the ones that are significantly smaller than the rest. For any of the other cells, I very carefully separate each tomato plant and transplant them each separately into larger pots. It's rare that I lose one when I do that, but it happens occasionally. I still end up with way more plants doing this than if I were to only select one per cell. But it also means that I end up with a lot of tomatoes - about 7 trays worth this time.
The key is being very, very careful with the roots. Massage the ball of dirt and roots gently and then carefully separate each tomato by holding the plant and gently wiggling it away from the others. Then you can plant each one of them. You might break a few plants when doing this, but once you get the hang of it you'll end up with more plants than if you saved one per cell.
Then when transplanting to the new pot, bury the stalk of the plant as much as you can. All those little hair-like things you see on the main stalk will turn into roots if they're in the ground. By doing this, you build a much better root structure for your plant, which means a stronger and healthier plant down the line. I always do this will my tomato plants so that they'll have a good start.
Make sure to water the plants once you're done, as it helps with the stress (plus you just moved the plant into dry soil). There are also nutrients you can buy that help with transplant shock, if you want to use that.