Preheat grill for medium heat. Place preserves, water, ginger, and mustard in a small saucepan. Cook until ingredients are well blended, about 3-5 minutes. Be sure to stir constantly so mixture doesn't burn. Place ham on grill and allow to cook for 8-10 minutes. Slather ham with apricot glaze and turn over. Grill for and additional 8 minutes, coating ham with glaze 3-4 more times.
While grilling ham, arrange apricot halves in a grill basket. Grill apricots for about 6 minutes, turning once. Coat apricots with glaze. Remove from heat and set aside.
Once ham is cooked, remove, let rest for 3-5 minutes. Slice and serve with glazed apricots.
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