Wash and pat dry the swordfish steaks; season each with salt and pepper; completely coat each steak with olive oil.
Heat a grill pan over medium heat; cook the steaks in the grill pan for 15 minutes, turning twice.
While the steaks cook, stir together the garlic, parsley, basil, arugula, and lemon juice in a bowl until evenly coated; spoon over the cooked steaks to serve.