Start by rinsing the swordfish steaks under cold water and patting them dry with paper towels. Season the steaks with salt and pepper to taste on both sides.
Preheat your grill to medium-high heat. Make sure the grates are clean and lightly oiled to prevent sticking.
In a small saucepan, melt butter over medium heat. Once melted, add freshly squeezed lemon juice and minced garlic. Let it simmer for a few minutes until the garlic is fragrant and the sauce slightly thickens. Season with salt and pepper to taste. Set aside.
Place the seasoned swordfish steaks on the preheated grill. Grill for about 4-5 minutes on each side, or until the fish is cooked through and easily flakes with a fork. Avoid overcooking, as swordfish can become dry.
During the last few minutes of grilling, baste the swordfish steaks with the lemon butter sauce using a brush. This will infuse the fish with flavor and keep it moist.
To ensure the swordfish is cooked to perfection, use a meat thermometer to check the internal temperature. It should reach 145°F (63°C) when done.
Once the swordfish is cooked through, carefully remove it from the grill using tongs and transfer it to a serving platter.
Drizzle any remaining lemon butter sauce over the grilled swordfish steaks and garnish with freshly chopped parsley or lemon wedges for added freshness. Serve hot and enjoy!