Sprinkle venison with salt and pepper.
Melt 2 tablespoons butter in large nonstick skillet over high heat.
Working in batches, add venison to a hot skillet and cook to desired doneness, about 2 minutes per side for medium-rare. Set aside.
Drain the mushrooms and save the liquid.
In fat remaining in skillet sauté mushrooms with garlic, stirring, until liquid mushrooms give off is evaporated.
Add a little mushroom liquid, demi-glace, Port, and Worcestershire sauce.
Simmer sauce until thickened and reduced to about 3/4 cup, about 5 minutes, and stir in vinegar and salt and pepper to taste.
Divide sauce among 4 plates. Place 2 venison medallions a top sauce on each plate.
