The Witch-King's Return
Matt T.

(what happened to the Witch King's ring I wonder? Mouth of Sauron was to get it maybe? Sauron wasn't one to waste Rings)

The Nazgul did not hold their rings, their rings held them :) Sauron had them, they did not wear them prancing around Middle-Earth, though they did of course bear them in their lives before they became wraiths. They were enslaved to Sauron through them. This is documented in Unfinished Tales and several other places I believe.

Therefore, there was no ring to recover from the Battle of the Pelennor Fields.