Preheat broiler. Place lemons, cut side up, in a small, non-aluminum baking dish and sprinkle with salt and pepper. Roast, about 6 inches below the heat, until very soft, about 20 minutes. The tops will darken and caramelize. Let cool in the baking dish.
Squeeze the lemon pulp and juice and scrape all the cooking juices from the baking dish into a strainer supported over a bowl. Force it through and add garlic. Whisk in rosemary and extra-virgin olive oil. Keeps up to 1 week refrigerated in a tightly sealed container.
Soak rosemary or wooden skewers in water to cover 1 to 2 hours.
Preheat grill or broiler. Skewer 2 tuna pieces lengthwise on each rosemary sprig and brush with marinade. Season with salt and pepper and grill, turning once or twice, to medium rare, 8 to 10 minutes, depending on heat. Serve immediately.