In case someone is interested,here’s how I make something like that (general technique):
Make a copy of your curved surface and give it a Subsurf Modifier (set at least one higher than what you are going to use on your surface) as a target for the Shrinkwrap (nothing special so far).
Outline the ‘seam’ for the cap and go into Edge Select Mode:

Press CTRL+B,, ‘mousewheel up to 3’ and select the middle ring.

Press V (that’s the magic touch…).
If you set up and enable your Modifiers, you get something like this:
