Prepare grill by lightly oiling grill grate over medium-high heat.
In a small saucepan, melt butter add lime juice. Salt and pepper the salmon fillets modestly on both sides. Place fillets onto grill, brush half of lime butter over salmon. Grill salmon for 2 to 3 minutes per side for medium-rare. Drizzle remaining lime butter over salmon before serving. Serve with pasta or rice.