I've got these Ikea spice racks in my kitchen, and the way I installed them they needed to be fastened to the wall for stability. I didn't want to drill the tiles, however.

Once again my answer is "recycling": I habitually salvage the magnets from dead hard drives. The spice rack is coated steel, the magnets are pretty strong and so I simply glued a bunch of them onto the tiles. Silicone sealant makes a decent glue for operations like that, and it's removable if need be. Problem solved.