Heat oil in a large nonstick skillet over medium heat. Add onion and garlic and cook, uncovered, for 10 minutes, stirring occasionally. Add peppers, salt and pepper. Cook for 5 minutes, stirring occasionally.
Add tomatoes, thyme and capers. Cook, stirring occasionally, for 7 to 8 minutes, or until tomatoes are cooked through and peppers are tender. Set aside.
Prepare outdoor grill with medium-hot coals, or heat gas grill to medium-high. Lightly grease grill. Brush swordfish with oil and season with salt and pepper. Grill for 7 to 8 minutes, turning halfway through cooking. Serve fish with the peperonata warm or at room temperature.