In a small bowl, stir together mustard, horseradish, lemon juice, tarragon, salt and pepper until well blended.
Heat olive oil in a large skillet over medium-high heat. Add salmon, skin side up; cook 5 to 6 minutes or until golden brown on bottom. Turn salmon and cook 4 to 5 minutes or until internal temperature reaches about 145 degrees. Spread some horseradish-mustard mixture over salmon pieces during the last 3 minutes of cooking.
Slide spatula between skin and salmon to remove skin. Serve salmon over rice if desired and drizzle with horseradish-mustard sauce; garnish with lemon slices if desired.