When we took down the drop ceiling (pictured below) we found the awesome beams and searched for the best way to showcase them, while still being able to run electric wire and heating ducts.
My brother-in-law figured out the system pictured above. Tongue and groove boards are cut to length and fitted between the beams. It's been quite the project putting it up, since nothing is level and many of the beams were hand hewed and have various bumps and grooves, making cutting and fitting the beams some what time consuming.

The boards are dropped about six inches from the bottom of the floor on the second floor, leaving room to put in some can lights. It was very exciting yesterday to have the lights installed and turned on (we did the rows with the lights first.)