Grill the zucchini. For zucchini planks, arrange in a single layer on the grill grates. Cover and grill without disturbing until grill marks appear and the zucchini is tender, 3 to 4 minutes per side. For zucchini ribbons, place the skewers on the grill grates (you may need to do this in batches depending on the size of your grill). Grill, turning occasionally, until the ends of the squash are charred, 4 to 5 minutes total.