Combine the soy sauce, canola oil, lemon zest, lemon juice, ginger root, garlic, and mustard in a bowl.
Pour half the sauce in a low flat dish that's just large enough to hold the swordfish in one layer.
Place the swordfish on top of the sauce and spread the remaining sauce on top. Cover with plastic wrap and refrigerate for at least 4 hours or preferably overnight.
Thirty minutes before you're ready to serve, build a charcoal fire or preheat a gas grill.
When the coals are medium-hot, brush the cooking grate with oil to prevent the fish from sticking. Remove the fish from the marinade, allowing some of the ginger to cling to the fish, and discard the marinade.
Sprinkle the fish generously on both sides with salt and place it over the coals. Cook for 5 minutes on each side, just until it's no longer pink in the middle.
Place on a platter, cover tightly with alluminum foil, and allow to rest for 10 to 15 minutes. Serve hot or warm.