Light a charcoal grill or preheat a gas or stovetop grill until very hot.
For the sauce, whisk together the lemon juice, olive oil, oregano, red pepper flakes, 1 tablespoon salt, and 1 teaspoon black pepper. Set aside.
When the grill is ready, sprinkle the fish with salt and pepper and cook over medium-high heat for 2 minutes on one side, then turn and cook for 1 to 2 minutes on the other side until almost cooked through. Remove to a flat dish, prick holes in the fish with the tines of a fork, and pour the lemon sauce over the fish while it¿s still hot. Sprinkle liberally with salt and pepper, cover with aluminum foil, and allow to rest for 5 minutes.
When ready to serve, place the swordfish on dinner plates or a serving platter, pile the arugula on top, drizzle with the sauce from the fish, and sprinkle with the grated lemon zest. Serve warm.
"Barefoot Contessa Foolproof" by Ina Garten (c) Clarkson Potter 2012. Provided courtesy of Ina Garten. All rights reserved.