- Pat swordfish dry with paper towels, rub with 1 tablespoon coriander, and season with salt and pepper. Thread fish onto three 12-inch metal skewers. Thread tomatoes onto three 12-inch metal skewers. Brush swordfish, tomatoes, eggplant, and scallions with 2 tablespoons oil.
- FOR A CHARCOAL GRILL: Open bottom vent completely. Light large chimney starter filled with charcoal briquettes (6 quarts). When top coals are partially covered with ash, pour evenly over grill. Set cooking grate in place, cover, and open lid vent completely. Heat grill until hot, about 5 minutes.FOR A GAS GRILL: Turn all burners to high, cover, and heat grill until hot, about 15 minutes. Leave all burners on high.
- Clean cooking grate, then repeatedly brush grate with well-oiled paper towels until black and glossy, 5 to 10 times. Place swordfish, tomatoes, eggplant, scallions, and lemon halves on grill. Cook (covered if using gas), turning as needed, until swordfish flakes apart when gently prodded with paring knife and registers 140 degrees and tomatoes, eggplant, scallions, and lemon halves are softened and lightly charred, 5 to 15 minutes. Transfer items to serving platter as they finish grilling and tent loosely with aluminum foil. Let swordfish rest while finishing caponata.
- Whisk remaining 2 teaspoons coriander, remaining 2 tablespoons oil, lemon zest, honey, garlic, cumin, ¾ teaspoon salt, ¼ teaspoon pepper, cinnamon, and nutmeg together in large bowl. Microwave, stirring occasionally, until fragrant, about 1 minute. Once lemons are cool enough to handle, squeeze into fine-mesh strainer set over bowl with oil-honey mixture, extracting as much juice as possible; whisk to combine. Stir in olives.
- Using tongs, slide tomatoes off skewers onto cutting board. Coarsely chop tomatoes, eggplant, and scallions, transfer to bowl with dressing, and gently toss to combine. Season with salt and pepper to taste. Remove swordfish from skewers, sprinkle with basil, and serve with caponata.
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