Preheat your grill to medium-high heat. Clean and oil the grill grates to prevent sticking.
In a small bowl, whisk together the olive oil, lemon zest, lemon juice, minced garlic, chopped rosemary, chopped thyme, salt, and pepper. This will be your marinade.
Pat the swordfish steaks dry with paper towels. Place the swordfish steaks in a shallow dish or a resealable plastic bag. Pour the marinade over the swordfish, ensuring both sides are coated. Let it marinate for at least 15-30 minutes at room temperature (or up to an hour in the refrigerator).
Remove the swordfish from the marinade, letting any excess drip off. Discard the remaining marinade.
Place the marinated swordfish steaks on the preheated grill. Grill for approximately 4-6 minutes per side, depending on the thickness of the steaks and your desired level of doneness. The fish should be opaque and flake easily with a fork when done. Avoid overcooking to maintain moisture.
Once grilled to perfection, carefully remove the swordfish from the grill using a spatula. Garnish generously with fresh chopped parsley and serve immediately with fresh lemon wedges on the side.