The kids all came running in from the garden shouting ,"Mom! Mom! Caterpillars!" And there on our overgrown and bolting dill plant were two very fat black, orange, and white caterpillars. Upon closer inspection I found a third smaller one. We cut off the dill stalks with the caterpillars and placed them in a Ball jar with a coffee filter to cover it. Out came the nature notebooks, followed by about a half hour of drawing and writing about the caterpillars. They were promptly named: Bippy, Snippy, and Nippy.
I've just been online trying to find out what kind of caterpillar we've got. At first glance I thought they looked like Monarchs, but Monarchs only lay their eggs on milkweed, not dill. Also, ours have orange spots, not just stripes. Then I found this picture on What's That Bug:

Apparently they are Black Swallowtail caterpillars, which makes sense, since I have seen the butterflies in our yard. They feed on members of the carrot family: carrots, parsley, fennel, Queen Anne's Lace...and dill.
So tonight we are constructing something like this:

(Ideal, since we just replaced the screen to the back door and had a scrap. The top and bottom are round cake pans.)
Here are the most helpful links I found on raising caterpillars:
Butterfly School
Science News for Kids: Raising Caterpillars
Bug Guide: Black Swallowtails
Bug Guide: Raising Caterpillars

