So Mom and Dad decided to let the caterpillars continue to eat the parsley as long as they wanted. This was an easy decision because they knew it would not be much longer. Yesterday afternoon one of them disappeared (later to be found to have gone all the way under the deck to the foundation of the house where it was preparing to turn into a chrysalis), and they watched as the other one cleverly swung its way onto the deck via a strand of dill - walking along it until the weight of the caterpillar caused the dill to bend down to the deck boards.
Dad set up a little environment for them within a terrarium, complete with a transplanted parsley, and a bunch of twigs. They are not eating and have settled into a spot on a twig each, and are starting to attach themselves to the twigs with some fine strands of silky stuff (see the lower one in this picture - it looks like a string around its neck).
From what Mom has read, it will be about 3 weeks till the butterfly stage, OR maybe they will become dormant and go all the way till next spring. They will take some pictures and keep you posted.
Dad has been calling one of the caterpillars "him" and the other "her": it will be interesting to see the colors to the butterflies to see whether he is right.