Cut and Dry the Salmon - Cut salmon into 4 equal portions, about 2 ½ to 3 inches wide. Wrap each fillet in paper towels, place it on a plate, and allow it to sit for up to 15 to 20 minutes to remove excess moisture.
Season the Surface - Brush each side of the fillets with olive oil. Season both sides with salt and pepper.
Preheat the Grill - Set the grill to high heat, 450 to 500ºF (232 to 260ºC). Clean the grill grates by carefully greasing them with the oil using a folded paper towel until shiny and glossy, about 5 to 10 times.
Grill the Salmon - Place each fillet diagonal to the grill grates and flesh-side down. Gently press down for maximum contact. Cover and cook until the salmon can be easily lifted off the grill, about 4 to 5 minutes. Check at 4 minutes, then every 30 seconds until the fish no longer sticks. Use a spatula if needed to release the flesh from the grates.Carefully flip and cook until medium-rare (125ºF) or medium (140ºF) doneness, about 3 to 5 more minutes depending on the thickness.
To Serve - Transfer to a clean platter and serve with lemon wedges.