Box turtles enjoy any type of insects and since they are very protein rich, you should also make sure to include insects into the diet of your pet turtle. You can either catch the insects yourself or give your turtle the chance to do so or buy them in pet stores or online. You can feed the following types of insects: mealworms, wax worms, super worms, earthworms, crickets, grasshoppers, beetles, slugs, snails, red worms, caterpillars and many more.