I think the best method is to construct a new end to the curve.
One method would be to use Bridge Curve. Select the existing curve and slide the start point of the bridge curve to somewhere along the existing one. (Or delete the trim and use the origianl curve end point). As second object change option to Datum and select the plane. Can then modify the setting to get the smoothness of transition you require. Then trim the trimed curve (if not used the original curve) to the start of the bridge curve.
Another option would be to create a line perpendigular to the plane then edit the curve end point to be G1 to the line.