Heat grill to medium. Transfer the peaches to the grill, cut-side down, and cook until grill marks appear, about 3 minutes. Turn and grill until the skin starts to shrivel and the peach softens, 4 minutes more.
Divide the peaches among individual bowls, placing 2 halves in each bowl. Top with the ice cream, drizzle with the honey, and serve with the lime wedges.