Place masking tape over the tile.
Replace soap dish tile wall.
Clean the area the new tile will not.
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 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.
Remove the broken soap dish a fractured soap dish may almost fall off the wall by itself.
Regrout after 24 hours.
Loosen the old grout if the soap dish has fallen entirely off the wall you can skip ahead to the third step.
The soap dish tile remove the grout around the tile with a grout saw.
Using a hammer and nail punch small divets into the tile in an x pattern.
Install a 1 4 inch masonry bit.
Install a replacement soap dish of either the retrofit style or in plain tile.