Heat 2 teaspoons of the oil in a large skillet over medium-high heat.
Season the steaks with ½ teaspoon salt and ¼ teaspoon pepper and cook to the desired doneness, 4 to 6 minutes per side for medium-rare. Let rest at least 5 minutes before slicing.
Wipe out the skillet and heat the remaining 1 teaspoon of oil over medium-high heat.
Add the tomatoes and ¼ teaspoon each salt and pepper. Cook, tossing occasionally, until beginning to soften, 4 to 6 minutes.