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Combine the marinade ingredients in a bowl and whisk until combined.
Pour the marinade over the swordfish steaks. Cover and refrigerate for 20-30 minutes, or up to 8 hours.
Preheat the grill to medium-high, and cook the swordfish steaks for 5-7 minutes per side.
Remove the steaks from the grill, garnish with parsley, and serve with lemon wedges.