Light a grill. In a small bowl, blend the butter with the diced pickles, tarragon and mustard and season with salt and pepper.
Rub the salmon with oil and season with salt and pepper. Grill over moderately high heat, skin side down, until the skin is lightly charred and crisp, about 3 minutes. Using a metal spatula, turn the fillets and grill until barely done in the center, about 4 minutes longer. Transfer the salmon to plates. Top with the dill pickle butter and serve.