Hi Mama... I raise butterflies in my home, and was so excited to see your post. I'd LOVE to find some swallowtails on my parsley!
Parsley is a butterfly host....so they will lay their eggs on it - thus bringing you baby and adult caterpillars. If you turn the leaves up, you're likely to find more eggs which will bring you more catterpillars. Here's a link to see what the eggs look like: Butterflies, Cats, and Chrysalides
If you scroll to about the middle of that page you will see a picture of what their cocoons look like - so maybe you can identify them.
Swallowtails do have quite a bit of enemies.... birds will eat the caterpillars...and ladybugs, ants, spiders, etc.. will eat their eggs... so if you have a bird feeder by your parsley - you might consider moving it to a different location to help protect the caterpillars. Here is another great website made by a man who raises swallowtails in his home: Berkeley's Anise Swallowtails
If you want to know how you can bring the next caterpillars you find into your home and watch them cocoon and turn into butterflies - PM me! I can help you do so successfully. I currently have about 15 cocoons in my home...and upteen cats, too.
It's a wonderful learning experience for the kids! Oh, and there's something really beautiful about releasing a butterfly!
(The government even offers grants to raise butterflies because many types are becoming endagered with all of the increasing polution and an increase in enemies that eat them before they can become butterflies.)