1/4 cup olive oil, plus more for grill and drizzling
4 (5–6-ounce) skinless, boneless halibut fillets
Kosher salt, freshly ground pepper
2 pounds mixed heirloom tomatoes, sliced
1/2 cup sliced drained hearts of palm
Torn basil leaves (for serving)
Prepare a grill for medium heat; oil grates. Finely grate 1 tsp. lemon zest directly onto halibut and lightly drizzle with oil; season with salt and pepper. Grill halibut, turning once, until browned on both sides and just opaque in the center, about 5 minutes.
Meanwhile, combine tomatoes, hearts of palm, and 1/4 cup oil in a medium bowl; squeeze in 2 Tbsp. juice from lemon and toss to combine. Season with salt and pepper.
Toss basil into tomato salad. Serve halibut with tomatoes and dressing spooned over.