In a small saucepan, combine vinegar, honey and salt; cook and stir over low heat until blended, 2 - 3 minutes. Reserve 1/3 cup mixture for brushing nectarines.
Bring remaining mixture to a boil over medium heat; cook and stir just until mixture begins to thicken slightly (do not overcook), 4 - 6 minutes. Remove from heat.
Brush nectarines with some of the reserved balsamic mixture. Grill, covered, on an oiled rack over medium heat until caramelized, brushing occasionally with remaining reserved balsamic mixture, 6 - 8 minutes on each side.
Serve with glaze and ice cream.