Check the quail for bones or feathers and place in mixing bowl. Add the pancetta, vinegar, olive oil, honey, and black pepper and toss to coat. Set aside and preheat the grill.
In a 3-quart saucepan, water and sage and bring to a boil.
Thread one quail, followed by one piece of pancetta, followed by one quail on each of four skewers and place on hottest part of grill. Cook 4 to 5 minutes on each side, until just pink at the leg bones.
Meanwhile, pour the polenta slowly in a thin stream into boiling water, until all is incorporated and polenta thickens, about 1 to 2 minutes. Switch to a wooden spoon, add the cheese, and cook another minute, until as thick as paste. Remove from heat and pour on to a service-ready cutting board. Pile skewers on top of polenta and serve.