Slice off the bottom and the green top of the pineapple. Stand pineapple on one cut end and slice off the skin in wide strips, from top to bottom. To remove the eyes, cut diagonally around the fruit, following the pattern of the eyes and making narrow, wedge-shaped grooves in the pineapple. Cut pineapple crosswise into 6 slices. Remove core; set aside.
In a small saucepan, melt butter or margarine over medium heat. In a small bowl, stir together lime peel, lime juice, honey, cornstarch, and ginger. Stir into the melted butter or margarine.
Cook and stir until mixture is thickened and bubbly. Cook and stir for 2 minutes more. Remove from heat.
Place pineapple slices on the rack of an uncovered grill directly over medium heat for 8 to 10 minutes or until heated through, turning once and frequently brushing with lime-butter mixture. Makes 6 servings.