He was on Great Performances last night.  It was pretty cool:

“Sting: Songs From the Labyrinth” features the works of composer John Dowland (1563-1626) performed by Sting and lute player Edin Karamazov. Included: “Come Again,” “Flow My Tears,” “Can She Excuse My Wrongs?” and “In Darkness Let Me Dwell.”

It is pretty somber stuff, but I like the renaissance style stuff sometimes.  It might be worth recording just to check it out.  There's more broadcast times (most are late night or early morning now) and more info on the Great Performance's website