Personally, I would use a bull nose ceramic tile to finish off the sills. You can find these in marble and other finishes. The bull nose edge gives that ready made curve downward, that finishes the edge. They're much cheaper also! That's just my opinion!
That's what I'd suggest to use, if you're set on this type of material for the sills!
Just keep in mind, that your home should be set on a permanent foundation if you have any type solid tile surface in your home.
Ceramic, granite and marble are solid surfaces. Perfect installations require no movement at all. Our homes are designed to move... they travel down highways at 55 miles an hour to get to the site. Please keep this in mind!
It can be done easily, but the upkeep, will much greater than a stick built.
Maureen
but would like to replace these sills with something more durable so i can put a plant on there without the worry of leaking or just in case I dont make it to the window quick enough when it begins to rain. Here in my area you can experience all 4 seasons in 1 day 
and the weather can take you by surprise. But I dont have any idea how to remove the old sill and if I would use marble, what would I use to fasten it. I see small nails in the current sill. All advice welcome. Thanks!
and want to protect it as much as possible and you folks have given me some great ideas. Now I need to choose the one to go with. Thanks bunches!