Cut tenderloin into 1/2" thick medallions. Place pork between plastic wrap and pound with a mallet to 1/8" thickness. In a shallow dish, combine flour, salt, and pepper. Coat pork medallions in flour mixture, shaking off excess.
Heat olive oil and 2 tablespoons butter in a large non-stick skillet over medium-high heat. Cook pork for 1-1/2 to 2 minutes per side, or until golden brown Remove from heat; place pork in a warm oven (200 degrees F.).
Return skillet to stovetop over medium heat; add capers and garlic, and cook for 1 minute. Add chicken broth, wine and lemon juice. Cook for 4 minutes, stirring frequently. Add remaining 2 tablespoons butter and parsley. Cook, stirring until butte is melted and sauce has thickened slightly, about 1 minute. Remove from heat
Pour half of sauce over linguini and toss gently. Pour remaining sauce over pork. Garnish with chopped fresh parsley, if desired.