Cement is a good idea, however if it is a reasonably large area say
over 6" wide you can have problems with adhering the tiles if you don't
let the cement dry for at least a couple of weeks before tiling (due to
cement shrinkage).An alternative I use somtimes,is to use diy type
filler eg Tetrion which only takes the night to dry. Regarding tiling
on the window board you could screw some 12mm wpb ply to it then tile
on top. This will lessen the chance of the board going rotten over time.