Since silkworms don't drink water, they get their moisture from the leaves so they must be fresh, not dried-out. Unless you want to change leaves three times daily, you need a covered container to raise the worms in. It should be almost air-tight to prevent leaves from drying out, but have small air holes for ventilation. Try a transparent plastic cake cover with the handle removed to allow air in through the screw-holes. The photo at the right shows one of these covers, which is about 14" across, plenty of room for about 50 fully-grown silkworms.
In California, inexpensive plastic cake covers are available from Smart and Final Iris restaurant supply stores. You'll want some sort of plate or tray under the lid, too. Make sure to empty the leaves and droppings out at least every two days or mold might start forming and kill your caterpillars.
To continue to the next stage in development, click on newborn caterpillars.