I have 3 flat screens (one doubles as a computer monitor)
one is on a swing arm, I swing it back into the cabinet the old CRT occupied and lay Bungee cords over it in an "X" pattern using eye bolts to hold the cords as the first responder suggested.
The other comes off it's mount and goes in the laundry basket atop the dirty laundry.. Well cushioned, face down
The big one up front is securely bolted to the frame with the very same brackets the original CRT was (Eventually it will be mounted on a door and the area behidn it used for storage).