Grease grill grate. Heat grill to medium.
Place potatoes in a single layer onto a greased double-thickness piece of aluminum foil, about 16 x 12 inches.
Drizzle with 1 tablespoon olive oil.
Season with salt and pepper.
Add 1 rosemary sprig.
Fold foil into a packet and seal tightly.
Repeat step, making another packet with the zucchini.
Grill potato packet, covered, over medium heat for 15-20 minutes or until potatoes are cooked but still firm, turning packet frequently.
Grill zucchini packet, covered, over medium heat for 5-7 minutes or until crisp-tender, turning packet frequently.
Let packets stand for 5 minutes.
Take care when opening the foil; allow the steam to escape.