Ye what Gilles has posted is pretty similar except the line will generally go from one side to another (not necessarily opposit side, may wind around the face and go to the side on the left for example). Rather than being a loop enclosed in the face.

Thanks for the help, I was expecting an email to let me know about replies, sorry for the delay. I'll have a go at what you said and see what happens. I'd say I'll have more questions!!

Ok so basically I'm looking to be able to create grooves in a 3d piece.

I have made the piece by hand, but now want to make a 3d drawing of it.

It is the Continent of Africa and the grooves are the boundaries of countries. I made them with a rounded router bit and did it by hand, the depth was may 1mm, so pretty small.

On the horizontal axis, the lines are pretty curved, few straight sections at all.

An easy example would be say get a 3d square, any size you want. In the top of it, I want a curved line (it would need to be 2 lines completely parallel actually, I reckon, say 2mm apart).
Then I want to be able to remove this line from the top of the piece to a depth of 1mm. Ideally with rounded corners at the bottom of the groove but not vital.

Any ideas?