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Depending on the width of the shank and the type of ring, standing the ring may not be the answer. When using wax, you don't want so much wax that it obscures part of the shank, or so little that the ring will tilt as you shoot it. I tend to focus-stack images of rings in order to get enough DOF and detail for larger print, so I stopped using wax because it softened too much from the molding and the lighting (with larger rings, anyway). Movement is also a huge problem if you need to take a series of shots using varied lighting (for the metal, for the stones, pave, etc.). I also run into movement issues when suspending jewelry like earrings. If you only need one shot, either method can be OK.
These days, though, I shoot rings on a pane of glass. I shoot from above the ring, at an angle that, when the image is inverted, will appear as if the rings is standing, and leaning slightly into the lens. For consistency, I reference the previous shot for placement and angle, since the ring's setting may be different, and produce a different angle.
Other considerations will be which position works best for setting up the lighting. Setting up diffusion panels to feather the lighting just right can lead you in one direction or another.
I haven't upped my game enough that I'd say my method is a sure thing, but I'm putting it out there as an option.