Preheat oven to 350°F.
Warm 2 tablespoons olive oil in a skillet over medium heat. Add 1 thinly sliced shallot and cook until softened, 3 to 4 minutes. Add 2 thinly sliced garlic cloves and cook for an additional minute, until softened. Remove skillet from heat.
Stir in 1/4 pound diced tomatoes, 1 tablespoon capers, and ¼ teaspoon salt.
Lay two 15-inch square pieces of parchment paper flat on a working surface and lay 3 lemon slices down the center of each. Place two 6-ounce fillets of halibut over the lemon slices and season each piece of fish with with ¼ teaspoon salt and a pinch of fresh ground black pepper.
Divide the tomato mixture evenly over each fish filet.
Gather the parchment paper at the top of each filet and fold it down until you reach the fish. Now fold up each side around the fish and crease tightly so that it holds. It doesn’t have to hold super tightly.
Place fish packets onto a rimmed baking sheet and bake for 15 minutes, until the packets are slightly puffed. Snip the parchment open with scissors and serve with lemon wedges.