Gently pat your salmon filets dry with a paper towel. Season generously on both sides with salt and freshly ground black pepper.
Place a non-stick skillet over medium-high heat. Once hot, add the olive oil.
Carefully lay the salmon filets into the hot skillet, skin-side down. Cook for about 3 minutes until the skin is beautifully crispy and golden.
Reduce the heat to low. Add the butter to the pan. If you're using fresh dill and grape tomatoes, add them now for an extra burst of flavor.
Using a spoon, gently spoon the melted butter and pan juices over the top of the salmon. Continue cooking and basting for another 3-5 minutes, or until the salmon is cooked to your preferred level of doneness (it should flake easily with a fork).
Carefully remove the salmon from the pan and place it on your serving plates. Drizzle any remaining delicious butter and pan juices over the top. Garnish with extra fresh dill and tomatoes if desired, and enjoy your healthy, flavorful meal!