Pat the swordfish steaks dry with kitchen paper. Season both sides with salt and freshly ground black pepper.
Heat a large, heavy-based frying pan over medium–high heat. Add the olive oil and heat until shimmering.
Add the swordfish steaks to the pan without crowding. Sear for 3–4 minutes on each side until golden brown and opaque in the centre (about 63°C internally).
Add the minced garlic and lemon slices to the pan. Cook for about 1 minute until the garlic is fragrant and the lemon slices start to caramelise.
Squeeze the juice from the remaining lemon half over the steaks. Remove the steaks from the pan and transfer to plates.
Sprinkle the chopped parsley over the swordfish and serve immediately.