Grease and preheat your grill. Use a very sharp knife to remove the skin from the salmon fillet and cut salmon into 1 1/2 inch pieces.
Thread salmon pieces onto your metal or wooden skewers being sure to keep at least 1/2 inch between each piece of salmon. (if using wooden skewers, be sure to soak them in water for 30 minutes prior to using so they don't catch fire on the grill)
Prepare your lime-butter sauce by melting your butter over medium heat in a medium size sauce pan. Once melted, bring to a boil and cook for 3-4 minutes until color starts to darken a bit.
Add garlic, lime juice, and lime zest to your melted butter and stir over heat for 1 minute. Remove from heat.
Brush salmon skewers with butter sauce. (you should have some leftover) Grill salmon for 6-10 minutes, turning throughout to ensure even cooking. Remove from heat and drizzle remaining lime butter sauce over salmon and serve immediately.
When picking out a salmon fillet for this recipe, I recommend looking for one that is thicker and has as close to an even thickness throughout as possible. This way the skewers salmon pieces are close to the same size and will cook evenly.