I dropped it in the kitchen and the bottle busted. We were able to get most of it off before it dried except for smears in the grout and tile. I am afraid polish remover will damage the ceramic.

Using nail polish remover should be okay. I shouldn't mess up the ceramic.

no it will not mess up the tile all of us women im sure have done the same thing i used 2 bottles of remover on the tile and grout and it is fine..

It won't I dumped an entire bottle of bright red polish on my white ceramic tile and it got into the grout. I used my non-aceton nail polish remover and got it all out of the grout and the tile. You have to keep moving the rag or cotton ball as it becomes saturated with the polish to keep from smearing it all over.