Heat grill to high. Cut swordfish and salmon into twenty-four cubes (about 1 1/2 inches each); thread against the grain on eight skewers, alternating with tomatoes.
In a blender, puree basil, oil, and garlic until smooth. Season with salt and pepper. Reserve half.
Brush kabobs with half of basil oil; season with salt and pepper. Grill until fish is opaque, 6 to 10 minutes, turning occasionally. With a clean brush, coat kabobs with reserved basil oil. Serve immediately.
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