To calculate the Z values along a line in Surfer, use the Grids | Calculate | Slice command. You will need a BLN file defining the line. This workflow will also give you the XY coordinates of each point along the line.  The steps are:

1. Create a vector file (like a SHP, DXF, or BLN file) of the line if you do not already have one. For information about creating BLN files, please see the article: How can I create a BLN file in Surfer?
2. Click Grids | Calculate | Slice. 
3. In the Grid Slice dialog:
1. Select the grid-based map from the Input Grid dropdown list, or click the Browse button to navigate to and select the grid file.
2. Select the base map containing your polyline from the Slice Line dropdown list, or click the Browse button to navigate to and select the vector file.
3. Check the Output to DAT box and give your DAT file a name
4. Click OK.
4. Click File | Open in Worksheet and open the DAT file in the Surfer worksheet. Columns A, B and C are the X, Y and Z values along the line.

Alternatively, if you have a worksheet with the XY coordinates of the points you wish to calculate the Z value for, you can use the Grids | Calculate | Point Sample command. Instructions for Grid Residuals can be found in the Help on the How can I find the Z value of a known XY point? page.

Updated February 2021