In a microwave safe bowl, combine butter & preserves. Cover & microwave on high for 45 - 60 seconds. Stir in lime juice, garlic & mustard until blended. Cool. Set aside 1 C for basting & serving.
Place salmon fillets in a large resealable plastic bag; add remaining peach mixture. Seal bag & turn to coat. Marinate for 30 minutes.
Preheat grill to medium heat.
Drain & discard marinade. Using long handled tongs, moisten a paper towel with cooking oil & lightly coat the grill rack. Place salmon skin side down on grill rack.
Grill, covered, over medium heat for 5 minutes. Spoon 1/2 of reserved peach mixture over salmon. Grill 10 - 15 minutes longer or until fish flakes easily with a fork, basting frequently. Serve with sliced peaches & remaining peach mixture.