Surfer can add the geometry created by the Measure Tool directly to the existing map as a new base layer or it can be added to an existing base layer. After measuring, in the Measure dialog, click Options | Save Geometry to Base Layer to add the polyline or polygon used for measurement to a new or existing base layer. After clicking Save Geometry to Base Layer the Destination Layer dialog is displayed.  Pick an existing layer, or type in a new layer name and press OK.

Saving the measurement geometry to a Base Layer in Surfer. 

Updated April 8, 2020