Choose a Roma tomato that is green or partially green in color. Select green tomatoes when they will not be used or needed immediately.
Place the green Roma tomatoes in a warm location. Choose a window sill or table that receives at least partial sunlight during the day if possible.
Arrange the Roma tomatoes so they are a single layer deep. Turn the tomatoes every day or so to promote even ripening and help prevent soft or damaged spots.
Allow the Roma tomatoes to slowly ripen and develop flavor in the warm and sunny location. Watch for the skin color on the tomato to turn from green to light red, indicating it is ripe.
Place the Roma tomatoes in the refrigerator once they have ripened. Put the tomatoes in the crisper of the refrigerator, if possible, to allow them to chill several hours before serving.