The technique that Ray Mears uses to keep his stone from moving around is to create a frame by hammering 4 small nails around the stone into a log. This works, but, over on the Equipped to Survive Forums, I picked up a better idea: simply cut up a bit of non-stick rubber padding.
This padding is sold in rolls and meant to be placed between carpets and hard-wood floors to prevent the carpet from moving around. The stuff that I use is actually meant to line shelves and drawers. The only different between it and the carpet padding is that the shelf and drawer stuff has smaller squares and a tighter mesh.
I find the padding to be much more convenient that the nails. It’s easier to deploy — you don’t have to take the (albeit small amount) of time to hammer in and then remove the nails; the pad works just as well on a rock as it does on a log; and the pad does not get in the way when sharpening, as the nails will sometime do.
For storage and transportation, I simply wrap the pad around the DC4’s sheath and secure it with a rubber band.
I still carry the small nails in the bottom of the sheath just in case, but I think the pad is a better way to go.