This is antique or at least vintage (family heirloom). It looks like it might be some sort of double-boiler? The bottom part is ~ 9.5" diameter and ~ 2" deep and appears to be ceramic-coated metal. The insignia on the bottom looks like a lion leaning on a coffee-pot with a "B" in it, and lettering under the stamp is illegible, except for the number 134. On the metal rim it says 'Patented May 23, 1899'. The top part is possibly aluminum, is less than 1" deep, and it is textured as shown, with no markings on the bottom. Handles on both are wood. Even when holding both in hand, these are not heavy. All ideas are welcome, as I am baffled.
Update 12/12: The enameled pan has been identified as a chafing dish, but the textured pan is still a mystery, so if there are any ideas on what it is or how it might be used, please feel free to share!
(click for full size)