I've moved numerous times with my many plants without incident The easiest way I've found is to water minimally (only enough so the first isn't loose) and cover only the pot in a grocery or waste bin size bag, very securely. Then cover with leaf bags (the really large clear ones) and tie them closed. Typically I'll put the already covered planter in the bag first and pull it up and tie it. I have a few that need two bags for height, I'll put one over top first, tie it snug, then the other under the pot, pulled up and tied over the upper one. If they need to be secured, smaller boxes and/or styrofoam work great. Longer/taller ones being on an angle has been fine too since they're bagged up really well.