Cut pork into ¼ inch slices and then pound thin by placing the slices between 2 sheets of plastic wrap and pounding thin with a mallet.
In a medium sauté pan (not non-stick) heat butter and olive oil over medium heat until light brown. Cook the pork slices in small batches so each slice makes good contact with the pan surface and browns well around the edges, approximately 2 minutes on each side. Transfer the slices to a warm plate and sprinkle with salt and pepper. Hold each batch of meat in a warm oven while working on another batch, but don’t allow the pork to dry out by keeping it in the oven too long. Also, watch the pan drippings carefully so they do not burn.
Remove the pan from the heat and add the balsamic vinegar, scraping the pan with a wooden spoon. Return the pan to the heat and add the port wine and the Sour Cherry jam. Bring to a low boil until slightly thickened. Spoon the mixture over the pork and serve immediately.