Preheat a barbecue for medium-high heat. Place the rack 12cm from the heat source.
In a blender or food processor combine the mint and parsley with the lemon juice, garlic, honey, olive oil, salt and pepper. Blend into a smooth paste. Spread the herb paste over the salmon fillets and allow to marinate for five minutes.
Remove salmon from marinade and discard remaining marinade. Lightly oil the grate then cook salmon for 2 to 3 minutes on each side, or until fish flakes when tested with a fork.
Brush the fillets with melted butter and garnish with lemon slices and mint sprigs before serving.