With a sharp knife, cut the fish into thin strips and arrange them on a flat saucepan. Sprinkle with lemon juice and marinate about 4 or 5 minutes.
Then drain and discard the juice. Put tomatoes in a bowl with olives, onions, capers, basil, olive oil, a little parsley, salt and pepper. Mix well with a spoon and sprinkle it over fish.
Garnish with lemon wedges and chopped parsley. Serve the swordfish carpaccio accompanied by toasted bread with garlic, olive oil and salt.