Rather than buying suction cups (for which I would subsequently have had no further use), I managed very nicely by using just a couple of strips of packing tape. Each strip formed a "handle" -- one on each side of the screen, same as you'd do with the suction cups.

There are various ways to manage this, I suppose, but in my case each strip began as a roughly 16 inch length. I folded it 180 degrees at the halfway point and allowed the two legs to stick to each other for about 4 inches. Then the two legs part company, turning 90 degrees but in opposite directions -- and that 90 degree point is where the tape meets the surface of the glass.

This works, but it is risky since I've seen it damage the screen coatings on some of the iMacs. Some of the older ones seemed to have softer coatings.