Scrape away any mess with the edge of the knife.
Repair cracked concrete window sill.
Resist the urge to keep touching and fiddling with the look of the smoothed caulking you will probably make it look worse.
Brush the sill with a soft brush to remove dust and dirt before applying the first coat of masonry paint after any of the following work has been done if required of course.
Remove the excess material build up on the putty knife.
Fix any small or medium cracks in your concrete window sill with caulk.
Use mortar mix on the block and replace the pieces.
If the sill is plain concrete it will not need to be painted.
However you should be able to purchase grey exterior filler which will be a close match to the concrete.
Any cracks can be sealed with the mortar mix or cement based caulk.
If the sill is painted repaint the whole sill as this will give an overall better finish.
Steel reinforcing bars are cast into the center of the sill to strengthen it.
Other option measure it all up make up a timber mould and cast a new one fix either a piece of half round dowel or sash cord to create the drip cast the cill upside down this method will be better than trying to cast in situ plus no weak joints.
Using a small putty knife starting at the window smooth the caulking flush to the sill.
If you have the pieces just clean off any loose mortar from the block.
Spread and flatten the caulk with a small putty knife.
What would be an appropriate material to fill it with.
Concrete has high compression strength but low resistance to bending tensile strength so the steel reinforcement is necessary.
Sand down the filler when it is completely dry.
I have an exterior concrete window sill that has a crack in it that i want to patch pic attached.
Dust from the sill will rub into the filler making it dirty but also blending it in with the rest of the sill.
Finishing the mortar joint.
I have on hand a tube of big stretch caulk and a tub of dap bondex ready mixed concrete patch.
Here is the smoothed caulking.