Some of the sources I have been reading say it is important to mist the cocoons (or chrysalis) a couple of times a week. Others don't mention this at all. What do you think?
Everyone has a different take of caring for the pupa stage, but here is mine:
When it comes to a cocoon or chrysalis, I try to leave well enough alone. If you are in a particularly dry climate, mist the pupa may be helpful to keep it from drying out. I keep a wet lab, with floors that are cleaned daily. My problem is more drying the place out rather than wetting it down. I have found that pupa can get "too wet". Mostly, it is the organic material to which they have attached their pupa that has a problem. The connected leaves, sticks, etc will begin to rot if they are kept too damn, breeding all sorts of fungus and bacteria. It smells bad, and fungus and bacteria just aren't good for us, or the butterfly or moth.
So, in short, if the container is bone dry a spritz of bottled (or otherwise purified) water can probably do them some good, but it is best to go easy on them.
I have a really good rate of success on most species. I move each chrysalis/cocoon into a 4"x4" plastic box with a lid. I pin the silk, stick (whatever the pupa is connected to) into a piece of open cell styrofoam that is attached to the lid with double sided tape. This hanging method is especially important for species that will need gravity to help stretch their wings when they eclose (emerge). Butterflies especially need their wings to dry while they are hanging upside down, otherwise the wings will not extend properly.