We had an unusually late frost after we had already transplanted our tomato starts outside this year. I covered the plants with canvas drop-cloths over the tomato trellises, but all the leaves and the top of the stems ended up dying. However, the main stems of the plants are green, and they've started to sprout new branches and leaves from their bases. Will the entire plant regrow and produce tomatoes, or should I just pull them up and start over? If they still have a chance, should I prune away any dead spots at the top of the stems? It's been about a week since it frosted, so I don't think there's any danger of it happening again. (Although the frost last week was over a week after the supposed "last frost date" this year.)
Tomatoes are on their own roots. If they are sprouting new leaves and branches they will be fine. Just work on making sure they don't freeze again.
This is true of virtually all herbacious plants btw. For woody plants if they are on their own roots, again you are usually ok but if they are grafted the leaves and branches are from the rootstock rather than the thing you want. This is an issue with grafted roses, fruit trees, and the like. However for non-grafted plants, the fact that it is resprouting means you should probably expect it to recover.
To piggyback on Chris Travers' answer, if you are seeing new growth then that's good news. I would expect it to recover if you are seeing new growth. Typically the late frosts we receive after our average last frost date aren't so severe as to kill the plant completely.
As to your follow-up question. I tend to take the position that the dead/damaged parts aren't going to benefit the plant and will typically prune them off carefully.