Install a replacement soap dish of either the retrofit style or in plain tile.
Replace soap dish tile wall.
Install a 1 4 inch masonry bit.
Loosen the old grout if the soap dish has fallen entirely off the wall you can skip ahead to the third step.
Remove the broken soap dish a fractured soap dish may almost fall off the wall by itself.
Regrout after 24 hours.
Place masking tape over the tile.
To help it shatter drill.
Use thin set and hold your new soap dish in place using long strips of duct tape crossing the new dish tile.
With a section of fine grit sandpaper in the 180 to 100 range roughen up the back of the soap dish and the ceramic tile wall.
The soap dish tile remove the grout around the tile with a grout saw.
The tape will help keep the drill bit from slipping and ruining an adjacent tile when.
Be careful when sanding the tile wall so that you are not extending your scratches beyond the soap dish s future footprint.