Rub steaks with olive oil, season with salt and pepper, and let stand at room temperature for 15 minutes.
Heat medium skillet over medium-high heat. For rare steak, cook filets until instant thermometer reads 130 degrees, about 10 minutes, turning once (for filets cooked to a greater doneness, turn down heat and increase cooking time). Transfer to serving plate and tent loosely with aluminum foil.
Place pan on medium heat; melt butter until it begins to brown slightly, scraping up any browned bits. Add garlic, and cook until fragrant, about 15 seconds. Add tarragon, swirling to blend. Pour sauce over steaks. Serve immediately.