Coining dies can be made in cad-cam for cost savings in the simpler designs, or by creating a 3d computer model and cut in the cnc machine. For the better, portrait-like designs the best way is to sculpt a clay model, then either scan and cut in the CNC or by traditional method.
We now have two options, the traditional way is sculpt a clay model at nine inches in diameter and cast it in epoxy resin. Then we use the finest machine available to reduce the size and cut the die into steel. (the same reducing machine that the U.S. Mint uses).
We have two automatic Janvier die sinking machines with high speed precision spindles used for this. The sculptors we have available are among the best. We can create a sculpture from artwork, or this can be supplied.
The second option is to sculpt a smaller model at considerable savings and three dimensionally scan into the computer, then cut the die on the cnc machine. Surfaces can be created and imported as stl files.