You can use "Spline on Surface" command
Mark and Troy,
Thanks, I'll give these a try. I suspect that they will do the trick.
Thank you Troy!
The Spline on Surface command is the way to do this. I was looking for a similar solution to the original poster; to sketch a 3D sketch onto an organic (was generated with a Loft feature) surface.
Tools > Sketch Entities > Spline on Surface
Check out these tools and see if any get you what you are looking for:
1. Insert>Curve>Split Line Using a 2D sketch and the "project" option.
2. Tools>Sketch Tools>Face Curves
Spline on Surface is extremely powerful, it can be a bit tricky putting relations on them though so you might need to manually tweak them until you're happy with them. But that's a small price to pay for its power.
Also, if you click on endpoints of a fairly curved face, your spline on surface might not be created - in that case try placing an additional point somewhere in the middle of the surface. Depending on the complexity I have found splines might need more points to pass through to successfully build on surface.