Zanash - I saw a magneticaly levitated platform once at a show once. The side load was supported by pins and bearings.

I have a different idea that picks up on ideas used in other isolation devices. - Control side loads with nylon fishing wire loopy things

Make two  platforms - One 20mm or so smaller  on both sides (when you look down).   glue opposing magnets on each face of supporting faces - however many you need  

screw  something like 8 sticky up pegs with perpendicular holes thro on bottom - larger board

Then drill an number of holes vertically in the smaller plate close to the  pegs you have fitted coming up from larger plate imagin a trampolin support . then connect pegs to the top plate by using nylon fishing wire tie off in a loop to make a trampoline affair then Bob (not sideshow) is your uncle.