Hi Jamie,
Well, your instincts were good! These are a bit different then say your luna or cecropia who make good solid cocoons. Many of the tufted cats incorporate their hairs in their cocoon which is what you are seeing as the loose cocoons. What you see inside is the pupa (equivalent of chrysalis of a butterfly) that looks like the moth with no wings. This is what it will spend the winter in before it emerges as a moth.
These have one generation in the north and 2 in the south (June-October) so depending where you live it may come out in the next few weeks/month or it will winter over and come out late spring early summer next year. For now I would just put a piece of screen, muslin or cheesecloth over the top secured with rubberband or string. Put it somewhere out of direct sun but where it can be exposed to normal day/night temps and day lengths (even more important than temps). If you are in the north then it will be a safe bet it will not be out until next year provided it is not exposed to excessively warm temps and unnaturally long days (indoors). You can winter it over in the crisper of your fridge, outside, in a garage on a porch, etc. If you keep in fridge it would only need a single drop of water every couple months. You can keep it in a small tupperware-type container. If you keep it in the plastic container in garage or somewhere you can spritz it lightly once a month or so just keep it safe from critters.
You are probably seeing a lot of these now as they may be wandering looking for a place to pupate.
here is a link with some photos of the pupa and cats. Where do you live? I am glad you are encouraging Sarah's interest in the 6-legged! 
American Dagger