Ahh, those pesky squirrels. It drives me nuts when they knock the pots over or they dig in them
If you have regular potting soil in those clay pots, you can try putting some gravel or small stones on top. That has completely stopped them at my house.
On another thread, someone suggested putting plastic forks upside down in the dirt to discourage the squirrels, so the tines are facing up. You might be able to do that in an orchid basket. Stick the forks in between the orchid roots, so that they're sticking out to make it uncomfortable for the squirrel to hang out in your basket.
Back to the clay pots, there are these Pot Klips that might work too. I have some, but haven't used them yet so I can't tell you for sure. They weren't terribly expensive though, and it might be worth a try. Amazon carries them, search for 'Flower Pot Klips', with a "k".
Hope that helps!