It is desirable to spin a tungsten when regrinding it, to get a nice symmetrical point. But that's hard to do with bare fingers because it get hot, and hard with gloved fingers because they're clumsy. I was trying to think of a good holder -- when I realized DUH I have a little tacklebox full of collet bodies and collets that the torch itself uses!
So I made a holder that uses these.
The collet body has a standard 5/16 x 24 thread so I drilled and tapped a piece of 3/8" OD brass tube. I drilled it to a depth of about 0.4", tapped it as far as the tap would go. Then I put a 1/4" 4-flute end mill in the tailstock chuck and ran that in for 0.5 inch to make a flat bottomed hole. I drilled it out the rest of the way to .187 because I had a piece of .187 OD brass tube on hand. That is the "handle", silver brazed into the hole. The ID of the tube is large enough to pass a 1/8" tungsten, the largest I ever use.
That's all there is to it! Select a collet and collet body of the size appropriate for the tungsten to be ground, insert the tungsten like I would when putting it in the torch, grind a nice symmetrical sharp point.