Place the swordfish steaks on a plate or cutting board and pat them very dry with paper towels. Trim off any dark bloodlines if you prefer, although they are safe to eat.

In a medium bowl or glass measuring cup, whisk together the olive oil, lemon juice, lemon zest, garlic, kosher salt, black pepper, smoked paprika, dried oregano, dried thyme, and red pepper flakes (if using). Taste and adjust seasoning; it should be bold and bright.

Place the swordfish steaks in a shallow dish or zip-top bag and pour the marinade over them, coating well. Marinate in the refrigerator for 15–20 minutes, but no longer than 30 minutes, flipping once if they are in a dish.

Cook the marinated swordfish on the grill, in a hot skillet, or in the oven. In all cases, aim to remove the fish when it reaches an internal temperature of 135–140°F (57–60°C) for juicy, just-cooked-through swordfish.

Preheat a gas or charcoal grill to medium-high heat (about 400–425°F). Clean and oil the grates well. Remove the swordfish from the marinade, letting excess drip off, and place on the grill. Grill for 4–5 minutes per side, depending on thickness, until opaque and just barely flaky at the center. Avoid moving the steaks too much so they develop grill marks.

Heat a large cast-iron or heavy stainless-steel skillet over medium-high heat. Add just enough olive oil to coat the bottom. When the oil is hot and shimmering, add the marinated swordfish steaks, letting excess marinade drip off first. Sear for 4–5 minutes per side until a golden crust forms and the center is moist and opaque. Reduce heat to medium if the garlic starts to brown too quickly.

Preheat the oven to 400°F (200°C). Lightly oil a baking dish and place the marinated swordfish steaks in a single layer. Spoon a small amount of remaining marinade over the top without covering them in liquid. Bake for 10–12 minutes, depending on thickness, until the fish flakes at the edges and is just opaque in the center.

Transfer the cooked swordfish steaks to a serving platter. If using butter, place a small pat on each hot steak so it melts into a quick sauce. Sprinkle with chopped fresh parsley and scatter capers on top, if using. Serve immediately with lemon wedges for squeezing over the top.

Check the thickest part of a steak with an instant-read thermometer; it should read 135–140°F. Without a thermometer, gently press the center—it should feel firm but still springy, and the middle should be just opaque and moist.