My tips are to go for a small variety, make sure its staked well, give it lots of care- make sure it doesn't run out of water in the smaller pot and as you may need to water more frequently, use liquid fertiliser (dilute).

They always say bigger pots are better for tomatoes… and not to overcrowd to maximise sun for best cropping. I've had self seeded tomatoes grow in "pots" tin can sized… so as long as you don't mind minimal fruit, any size is actually ok.

There's no simple hard limit, as the problems of smaller containers and varieties of peppers and tomatoes are diverse. I've been growing multiple tomato varieties (including Roma, Celebrity, Early Girl, and Patio) for a few years in cheap plastic pots 10.5" diameter at the base, 14" diameter at the top, 12" tall, with conical wire cages to contain & support the plants. For all varieties I grow except the "Patio" strain (which is specifically bred for containers) these pots are near the bottom limit on size in 3 ways:

1. Stability. Varieties that grow tall and produce well get top-heavy as they set fruit and can be tipped quite easily by a bit of wind or endemic vermin (i.e. squirrels, here in the Midwestern US.) Ceramic pots with more weight obviously would have this issue less at the same size, but
2. Water retention. Even with a "moisture control" potting soil the full-grown plants can suck every drop from their fully saturated containers in less than a day even in non-extreme (90°F/32°C) summer heat.
3. Foliage density. The impenetrable mass of stems, leaves, and fruit in the lower half of the plant can prevent rain from reaching the pot and hides fruit from sight and/or easy picking access.

However I must admit that the tomato-breeding wizards did quite a trick with Patio, a variety I'd resisted until this year, when I got one out of resignation at the generally thin collection of started plants available locally. It is much more of a squat stout Hobbit of a plant, not really needing its cage and never showing any signs of dehydration all summer. It has foliage density issues, but they are entirely due to its nature, not from caging it into a tight space. This morning I discovered that buried in the heart of its lowest branches there's a perfectly ripe 2" fruit that has no 2" path to the outside. A tragedy, as the fruit are better than I had expected but less prolific than my others.

I guess the short version is: select your varieties carefully for small containers and be ready to have a higher effort/yield ratio.

Thanks everyone for your comments. All of our tomatoes range from miniscule (wild cherry, lemon drop) to medium size (green zebra, jaune flamme) and we're not trying to grow anything like a slicing tomato, so I think they're all pretty container-friendly to start with. I think I'll aim for the 12"-14" pots (which is what we used last year, with decent success) but maybe where I have two of the same variety, I'll put one in a 10" pot and see how it goes.

Here in Melbourne in the summer, where it's regularly above 90F/32C, and sometimes up to 115F/45C we water the tomatoes twice daily in any case. It looks like this year our garden area (a semi-enclosed courtyard-ish space with lots of vertical stuff growing up the walls) will be moderately humid and maybe able to retain some of its moisture, compared to previous years when we had less stuff covering the fences etc. The climate overall seems to be getting a bit more humid in the summers anyway, I think; I really ought to check the climate data on that, but that's definitely the impression I got. Which is not to say actually humid, but not completely parchingly dry, in any case.

Well, I guess the best we can do (short of having more money to throw at it) is experiment and see what happens.

I've had luck with Red Robin dwarf cherry tomatoes in 8" pots. It's a hybrid variety that only grows 18" tall. I'm also having a lot of luck this year with the Little Prince cultivar of eggplant, which is a container variety that I tried on a lark. I do have to water every day in summer – late August in my area was consistently 95F, so if you get either variety, you might want to water twice a day.

I've also grown some Hatch green chiles in smaller (8-12 inch) pots this year. They're pretty heat tolerant, as they are a variety from southern New Mexico, which is a desert climate. I don't know if you can get the seeds shipped to you though, since the variety isn't well known outside of a small region in the USA.