How can I find the highest path of a DEM or contours file within an area?

Hello,

I would like to create a polyline from one specified point to a target point. In between, I'd like to the vertices to fall on the highest point of elevation of that Y coordinate.

Essentially, this will be the highest path for that area - or highest profile for this extent.

Has anyone had luck doing this in FME or another program, like ArcGIS?

Thanks!