I wanted to share a bit of new vs old photo results. Both the coin images are of the obverse of the 1876.
I set up my equipment the same way I usually do for macro photography of miniatures and other really small objects. I have a 105 mm f/2.8 VR Macro lens for my D600 and I added the 2x teleconverter so I could shoot really close in to the coin - having the coin fill most of the frame for really high resolution images - while still staying far enough back that I didn't get in the way of my light. I set up 2 speedlites. I initially was going to use both and have them behind the diffusion panels of the shadowbox but that was killing the luster in the images. I ended up just using one speedlite with a 1/128th full power setting undiffused. That gave me the results I liked the best. Using a small LED flash light to shine a little light on the coin made it much easier to autofocus with the lens. It's fairly dark in the shadowbox and the 2x teleconverter limits the effective aperture of the lens, making it hard to get enough light in for the autofocus to succeed without a little help. The circle of light projected by the flashlight also made it easier to keep the coins positioned consistently when swapping them out. Since the light from the small flashlight is so week it doesn't significantly impact the final image - the much more powerful speedlite dominates in the 1/100 of a second in which the image is taken.
Hopefully writing all of this down here will give me something to reference and help me remember later when I want to do this again. I'm including a picture of the set-up on the floor of the room I use as a home-office for now. I suppose it might be easier to do these things if I just set all of this up on a table and didn't force myself to flatten myself out on my stomach on the ground but... hey, I'm still fairly young (31) and don't have trouble getting back up... yet.
I was able to basically stand the slabs on their edge with them leaning ever so slightly back on the back of the shadowbox in some cases.
I think the new shots have much better detail, especially in his hair, beard and the field of the coin. They also look a lot sharper overall.
I'm not sure how this compares to how most others do it. Most of my camera equipment - except for the macro lens itself - was purchased for portrait and event photography and I generally find myself putting the same equipment to use here. I'd love to get a really nice lens-mounted ring-flash one of these days. I think that would provide the best and easiest lighting for something like this. But so far I just haven't been able to justify the cost.