Restoring marble windowsills

[diy-diy]

I am in the process of renovation of my 20yr old apartment. Paint wall, ceiling, sanding floors etc. Not sure though what's the best way to restore windowsills, made of some marble like stone and look rather used (see photo). Looking for cost-efficient approach...

 

[Cork-Guy]

I can't tell from this picture, but is that chipped or just run-off? You could replace it with another stone slab for the cost of the stone itself... obviously marble would be the most expensive, but there are other solutions.