Season the pork medallions with 1/4 teaspoon of salt and pepper. Heat 2 teaspoons oil in a large nonstick skillet over a medium-high heat and cook the meat until there is just a slight blush in the center about 3 minutes per side. Transfer the meat to a plate and tent with foil.
Add the remaining teaspoon of oil and the shallots to the pan and saute until they begin to soften, about 1 minute. Add the chicken broth, balsamic vinegar, the remaining 1/4 teaspoon of salt and the cherries and cook until the liquid is reduced by half, about 4 minutes. Season with salt and pepper, to taste. Pour the sauce over the pork medallions and serve.