Measure the top edge of the sheer curtains with the tape measure, add 1 inch for seam allowance and note the measurement. Cut a length of the stiffened tape to match the adjusted measurement of the curtains.
Position the stiffened tape along the top edge of the sheer curtains on the backside of the fabric. Align one long edge of the stiffened tape so it comes within about 1/8 inch of the top edge of the curtains. Turn under the raw edges of the tape 1/2 inch on both ends, ensuring that the cords protrude out from the ends of the tape. Pin the tape in place along the curtains with the straight pins.
Thread the sewing machine with thread that matches the sheer fabric of the curtains. With the thread matching the fabric and the transparency of the stiffened tape, the tape will be invisible along the top edge of the sheers.
Sew the stiffened tape to the sheer curtains, placing the first stitching line 1/8 inch below the top edge of the tape. Sew another stitching line 1/8 inch above the bottom edge of the tape. Remove the pins.