Heat grill to medium-high. Once it is hot, clean the grill grate with a wire brush. Just before grilling, oil the grill grate.
Soak 8 skewers in water for at least 15 minutes.
Fill a large saucepan with 1 inch of water and fit with a steamer basket; bring the water to a boil. Place the potatoes in the basket, cover, and steam until tender, 12 to 15 minutes; drain.
Toss the potatoes, halibut, artichoke hearts, scallions, oil, ½ teaspoon salt, and ¼ teaspoon pepper in a medium bowl. Thread onto the skewers and grill, turning occasionally, until the halibut is cooked through, 6 to 8 minutes.
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