Make the marinade: in a shallow non-metallic dish, combine 1/2 of the oil with the orange and lemon juices, garlic granules, salt and pepper. Turn the swordfish in the marinade, cover and leave too marinate in the fridge for 1 hour.
Make the orange relish: chop the orange segments into bite-sized pieces. In a bowl, combine the orange segments, the remaining oil, dried basil and season with salt and pepper to taste.
Remove the swordfish from the marinade and reserve the marinade. Place the fish under a hot grill and cook for 5 minutes on each side - basting once or twice with the marinade until the flesh is opaque and flakes easily.
Serve hot with the relish, some new potatoes and greens.