I do the same thing!
For shorter plants, like seedlings, you can use the web trays that you often get when you buy a flat of annuals. I put the seed trays/seedlings in one, the turn another over the top and twisty tie it on. Truly a life-saver from the marauding squirrels and chipmunks!
When you use the trays/baskets directly on the ground, a few landscape fabric pins work well to hold them in place.