Heat oil in a large nonstick skillet over medium heat. Add eggplant and cook, covered, for 8 minutes, stirring occasionally. Add garlic and cook 1 minute. Stir in tomatoes, salt and red pepper flakes. Simmer 10 minutes, covered, stirring occasionally. Tear in basil leaves.
Meanwhile, heat grill or broiler to medium-high. Cut each swordfish steak in half and season both sides with salt and pepper. Grill or broil for 4 to 5 minutes per side, until fish is cooked through.
Spoon sauce over fish and serve with pasta, if desired.