Purchase different size foam pads, used to put under furniture (sliders), at Home Depot, or Lowes. Get the ones without the sticky backing. These are the small ones.
 

These are the tools I use. Two different sizes of Xacto knives (be careful) and a pencil.
 

This is the small pad.
 

Push your wood-Henge into the foam pad and hold for a few seconds To create a mark that you can then cut out of the foam.
 

The mark.
 

I will trace the mark with a pencil, especially if I am creating numerous cuts at once.
 

Using the large blade Xacto, cut out the sides. I use another old pad underneath (as can be seen in the next photo) to cut into it as well so I do not stab myself!
 

Next step is to use the small blade and go over the cut ensuring you have gone totally through the pad.
 

Also, cut the ends with the small blade.
 

With the reverse end of the Xacto blade, push out the cut piece and then clean up and leftover shavings remaining.
 

Fit your Wood-Henge into the hole. It will push outwards in the foam and create a smooth edge.
 

Example of a small stand.
 

Example of a large stand.
 

Example of a tiered large, medium and small stand.
 

Other examples
 

Example of a multiple stand artistic arrangement resting on Ocotillo cactus wood.