Cracks in concrete window sill - best way to fill/repair pls

Old house. Has cement/concrete window sills. Some show cracking and 'peeling', like the one in the attached picture.

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Ideas please to fill/cover these cracks to give them another 20 years of life?

I clearly need to stop water getting in there and making in worse. The sill seems pretty sound structurally. Even those cracked edges aren't really loose - and I don't want to pull them off unless I have a plan for repair. I don't need to achieve perfectly flat results (ie bumps or ridges are ok). I don't really have access from outside (the one in photo is 2nd floor).

I was wondering about using a tile adhesive - ie a latex modified cement mortar. And then lots of paint.

Or just a caulk. (And then lots of paint.)

Or a regular cement mortar mix? (maybe made a bit sloppy so it can get into the cracks somehow?)

Help please.

Thanks in advance.

What about the external tiles to put on?? should manage from outside

I clean some old sills and boarded up against the front edge then poured in 8-10mm of self levelling compound , worked a treat and looked like new.Rounded of the front edge just before completely set.

foxhole said:

... then poured in 8-10mm of self levelling compound ...

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Nice idea. But don't I want a reasonable slope downwards (outwards) for runoff?

Yes make the levelling compounds thick enough not to run down the existing slope, you still have run off. I smoothed off with a plastering float.