Soften butter (do not melt), then whisk in mustard, sugar, and tarragon. Set aside to allow flavors to meld while fish is grilling. (Sauce may be prepared ahead of time and refrigerated. Warm to room temperature before serving.)
Grill or broil salmon. Fish is done when it flakes easily with a fork.
Serve hot with accompanying sauce. Sauce may also be used to baste fish during the final cooking stage.