yippee1999, there is an S-shaped mounting bracket - made of flat metal stock - and bent to loop over the window sill and, on the outside, bent twice to form a 'cradle' to hold the planter.
Two or three of these will support a window planter.
The only disadvantage is that the window and screen will not form a tight seal with the window sill.

thanks...yes, what you describe is exactly what I was thinking of and looking for but I can't seem to find it anywhere online. All the sides just seem to have brackets that you mount direcly to the outside of the building by drilling them into the outside wall.

Anyway, I just realized that....I couldn't use an S bracket anyway! Unfortunately, because I live in a very modern building, the windows we have don't open up and down, but side to side. So unless I plan to have my window open 24/7 to allow room for the S bracket, well....and S bracket obvioously can't work for times when I want to have my window shut, as the S bracket will preven the window from closing, even part way...

Oh well...guess I just have to give up on a window box...

Side to side, hmm?
You might have to rig up something weird, but I bet there is a way to do this. I would like to do it too. (I have the same situation as you. Except I don't have an outside ledge on my windows.)
Do you absolutely need a screen? If you're in the city like me, there shouldn't be too many insects. (Plus it would be easier to tend the planter without one.) Maybe instead of a screen you could wedge a small but sturdy dowel in the the window frame and anchor the planter to it.