What's the best way to store a tomato that has been cut?

freeze it. you don't believe me but it actually works. it's better to freeze a whole tomato but still it's good even sliced or diced. you don't have to defrost, just put it into you soup or cook withfried veggies.
it works. try it.

Clear plastic container with lid. Stays fresh and unslimey.

In your stomach
... Just kiddin'!

There's no really good result in storing cut tomato. But, I'd coat it with oil, equivelant of marination

If I'm going to use the tomato in the next 20 hours or less, I'll put it cut side down on a plate, then cover it with a cotton cloth to keep the flies out, then leave it out on the counter. Longer than that, I might put it in the fridge, but after about 30 hours it tends to get either weird texture or moldy, so I end up regretting it.

My preference is to make leftover tomato into a small salsa with shallot or mild onion (1 part onion to 4 parts tomato), chili flakes or chopped fresh chili to taste, salt and lime juice. Then put it in the fridge. Just a tiny bit of salsa can really perk up a meal.

Or slice the rest of the tomato how you want it tomorrow, mix with small splash of lemon juice or apple cider vin. Then put in a lidded glass container in the fridge - lasts about 4 days for me that way.

If you garden, you could always scoop out the seeds and save them (either by drying or fermenting) for next spring. An heirloom should by definition come true to seed, otherwise it's a modified or hybrid imposter. Then put the fleshy bit in the dehydrator or sun to dry, or better still greek salad.

I have glasses with lids. I feel tomatoes stay freshest simply placed inside, and used within a day or two. (Bought glasses on Amazon.

I would wrap it and refrigerate it for as short a time as possible.

Well if you must, then wrap tightly in Saran with cut side down and place is veg bin.
East ASAP!
Good luck
irina

I've never enjoyed a tomato that's been in the fridge, so I usually just slice up the rest and drizzle with olive oil, S+P and garlic powder and eat it. No one ever said eating more tomato was a bad thing, right?

If you're intent on saving it, though, here are some ideas: http://www.thekitchn.com/how-should-i-store-leftover-to-120910