Is there a tool to cut cherry tomatoes in half? Since they are so regular it should be possible to build such a machine.
Alternately, what can I do to improve my speed and accuracy when halving them with a knife?
Yes there is. It's called a knife. I use a Shun 10" chef's knife, but you could certainly make do with a much cheaper one.
When attempting to slice a lot of regular sized items, if you're not all that picky about the orientation of the cut (eg, if it's through or perpendicular the line between the blossom and stem), you can do the following, if you have a well sharpened knife that isn't going to slide on the skin of the tomatoes:
If you're nervous about cutting yourself, and you have plates that have a bit of a lip if you flip it over, you can put a plate down, upside down, fill the center with items to be cut, place another place on top, then while holding the plate down with light pressure, slice between the two plates.
I've found here: http://www.biggirlssmallkitchen.com/2012/06/streamlining-tomato-halves.html great advice to
Take two lids off any size food storage container you find fitting. Fill one with as many grape tomatoes your heart desires. Place the second lid on top facing down. Take a serrated bread knife and cut the tomatoes in half between the lids. Mine is in fact a 13" so I can cut about 12 boxes of cherry tomatoes in half in under 2 minutes.
Serrated knives leave scar marks in soft bodied foods, like this one, so if you are using it for presentation then this is not an option.
What you can do is take two small cutting boards, or two small straight edge items, shorther then the length of your blade. Fit, in a single file line, as many tomatoes as you can between the boards, use them to press against the fruit so hold them still then under a bridge made by your hand cute the tomatoes.
I use two six inch cutting boards which fit about 7 cherry tomatoes and a 7" non serrated blade. Once you get good with it you can cut like 200 a minute or more if you are really good.
Even better for any tomatoes a Serated Knife (one with ridges such like a bread knife).