Mechanical stages are most useful during photography, especially at higher magnifications. It's much easier to move a coin into position to photograph with an XY stage than it is by hand.
@Insider - I see your point @rmpsrpms - I see your point Hmmm....In that case two microscopes well-positioned and a swivel chair solve the problem!
I use a Zeiss rotating microscope stage (presumably from an old polarizing microscope) with mechanical X/Y controls for coin photography. With some setups, it may be possible to rotate the camera on the bellows, but it's easier to just rotate the stage and use the X/Y mechanical positioning.
If that stage could tilt on the "Z" axis and/or if the neck of the scope could (in concert with the light source somehow) that would be cool! Does that exist? Did we just invent something? I want some dibs! - Triple Axis Triscope with mechanical stage and swiveling neck. Surround view (instead of surround sound).
Hobby shops have holders with two alligator clips. Pad the clips and you can position the coin any way you wish. Since hobby shops seem to be a thing of the past...try the Internet: alligator clip hobby holder.
Getting warmer - There could be a holder or something to set the coin into so that the clips would not hide parts of or scratch the coin. But even such a holder would still obscure at least two tiny places the edge of the coin. Maybe the coin harness/holder is itself transparent and perhaps even magnifying.
Take 1/2 of a plastic capsule that the mint uses for coins and hold that with the clip. Set the coin inside. The edges of the container will keep the coin from falling out - even at steep angles. One that fits an Eagle should hold most sizes OR have several different sizes of capsules. Show us a photo if you make a holder of some kind.
"Helping hands vise." I have one of these in the basement I use for non-coins now and then. You can get them that have magnification and lights, too. American Science & Surplus has such a beast. They also have LED 10x loupe glasses (only doublets, not triplets, but also only $8.50). Wear these with a hood over your head and look like an albino Jawa.
I'm not sure what you are all attempting to do. The way I see it, for varieties under magnification: For direct-viewing under the microscope (during searches or attribution) it's better to hold the coin by hand so it can be held at an angle to the light, etc. For photographing under the microscope (to document a find) it's better to hold the coin flat and to adjust the lights to emphasize highlights and shadow details. Is this search for some way to hold the coin targeted at searching or photographing? Or maybe is it targeted for full-coin use rather than for varieties? What is the goal?
@rmpsrpms Someone said he (assuming he) was going to look for a microscope for working with his coins and was planning to see what bells and whistles he might want. I asked if he might get a mechanical stage and then we were discussing shortcomings and pluses of using one for looking at coins. We started brainstorming a bit. I think we finished. (Sorry if I was annoying. When I become so, simply bring it to my attention and I can stop). Thanks.
There a few ways to get this: 1) Universal stage (for microscopes) -- usually very expensive, but they do come up from time-to-time on eBay. 2) Goniometer, perhaps 2 one on top of the other to get two-axis tilting. Some macro photographers use these, especially for things like insects, etc. 3) Tilt-shift bellows -- this is like tilting the neck (sort-of). In my case, I can slightly tilt the whole stage by using thin shims under the mounting bolts, etc. I used this only to get the stage as close to square with the bellows as possible, then don't change anything. Normally, you'd want the coin exactly level with the camera and lens, so that you get he whole coin in focus. There is a pseudo-axial technique with a tilt-shift bellows or adapter where you can either shift the lens and coin and bounce light off the coin back up through the lens, or tilt the lens (or even the camera with an upside-down bellows) and coin to bounce the light off the coin. I've tried the shift method, but never attempted the tilt method -- scared off by having to match up all the Scheimpflug angles. I've moved on to a true diffuse axial technique for shiny problem coins. This uses a 45-degree 50% silvered glass/mirror and all that. It's easier to get extremely uniform illumination across the whole coin, which is needed when shooting through slabs.
I'm very low tech...I have a cork on my microscope stage. The coin is flat on the top of the cork and I can rotate the coin w/o touching the coin. If I wish to tilt the coin, I put a toothpick under one side of the cork. Need more tilt? Use something thicker.
I use a goniometer to tilt the coin toward the light, and a tilt adapter at the camera to compensate the tilt for good depth of field.