Cut salmon into 4 equal portions, about 2 ½ to 3-inches wide.
Wrap each fillet in paper towels, place on a plate and allow to sit for 15 to 20 minutes to remove excess moisture.
Brush each side of the fillets with olive oil.
Season each side with salt and pepper.
Preheat grill over 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.
Place the salmon in a diagonal to the grill grates flesh side down. If the skin is already removed, that side should be facing up.
Gently press the salmon on the grill 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 gently release the flesh from the grates.
Carefully flip the salmon and cook until medium-rare (125ºF) to medium (140ºF) doneness, about 3 to 5 more minutes depending on the thickness.
Transfer grilled salmon to a clean platter and serve with lemon wedges.