Rinse and pat dry swordfish. Place fish in a glass baking dish. In a large mixing bowl, whisk together white wine, soy sauce, mustard, ginger, garlic, sesame oil, olive oil and 1/4 cup lemon juice. Pour sauce over fish, cover and refrigerate for several hours or overnight.
Remove swordfish from marinade; reserve marinade. Use a sharp knife to cut pockets into the sides of the swordfish steaks.
In a large bowl, toss together arugula, tomato, 3 tablespoons olive oil and 3 tablespoons lemon juice. Stuff swordfish with arugula mixture and seal with toothpicks.
Place marinade in a small saucepan and cook over high heat until reduced by half.
Heat a grill or broiler to high heat. Grill swordfish for 5 minutes on each side. Spoon reduced marinade over swordfish and serve.
