In a small bowl, stir together goat cheese, honey and minced rosemary.
Place a 1/4-inch plain pastry tip in a small pastry bag or in snipped corner of a self-sealing plastic bag; fill bag with goat cheese mixture. Poke bottom end of each fig with pastry tip and squeeze about 1 teaspoon goat cheese mixture into each fruit.
Drain rosemary branches. Drive a metal or wooden skewer through center of each fig, then remove. Thread 2 to 3 figs onto each rosemary branch.
Grill figs over medium heat, turning constantly, until they just begin to brown, 5 to 8 minutes. Remove from heat and place whole branches on serving plate, or cut branches between each fig and serve individually.