Place a ladder against the wall at the position you've determined for the pergola's end board. Start at one end of the location and measure and mark a spot every 16 inches onto the stone wall.
Drill 3-inch-deep holes into the walls at the marked locations with an impact drill equipped with a carbide tip. Be sure to wear safety glasses as you do this.
Place a masonry anchor into each of the holes and tap them in flush with a hammer.
Cut a 2-by-10 inch board to the length you've planned for the pergola's end piece board. Drill holes through the board every 16 inches that correspond to the location of the anchors on the wall.
Place the board into position and insert lag bolts with washers into each hole. Tighten them down with a socket wrench until the board is firmly attached. The end piece is now ready for the addition of the pergola's mounting hardware and cross pieces.