to find a possible segment to match to, offset the vertical surface with 0.02 in both direction and intersect with the circular surface you get two edges which indicate the boarders. dup edge the outer rim and trim the rest of it off. you have your curve which you will match the surface to.
now untrim the outer rim and intersect with the surface you get the upper edge and trim the upper part off with it make dup edge on the other 3 edges and use EdgeSrf to create a matchable surface. now just match the upper part of this surface with the curve you created before.
SurfaceMatchingWTrims.3dm (56.6 KB)