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1
Put oven rack in middle position and preheat oven to 425F.
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2
Stir 2 tablespoons lemon juice into a large bowl half filled with cool water, then drop in juiced lemons.
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3
Cut 1 inch off top of 1 artichoke with a knife.
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4
Bend back outer leaves until they snap off close to base, then discard several more layers of leaves in same manner until you reach pale yellow leaves with pale green tips.
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5
(Dip artichoke in lemon water occasionally to limit discoloration.)
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6
Cut remaining leaves flush with top of artichoke bottom using a sharp knife, then remove choke by pulling out purple leaves and scraping out fuzzy layer with a spoon or melon-ball cutter.
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7
Trim 1/4 inch from end of stem, then trim base and side of stem with a vegetable peeler or sharp knife.
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8
Drop artichoke into lemon water.
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9
Trim remaining 3 artichokes in same manner.
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10
Drain artichokes, pat dry, and cut each into 6 wedges.
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11
Arrange artichokes in 1 layer in a 13- by 9-inch glass or ceramic baking dish.
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12
Stir together 3 tablespoons oil, 2 tablespoons lemon juice, 1/4 teaspoon salt, and 1/8 teaspoon black pepper in a small bowl and pour over artichokes, turning to coat.
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13
Cover dish with foil and roast, turning artichokes over once or twice, until just tender, 20 to 25 minutes.
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14
Leave oven on.
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15
While artichokes are roasting, rub fish with 1 tablespoon oil and sprinkle all over with 3/4 teaspoon salt and 1/4 teaspoon black pepper.
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16
Remove foil from baking dish and arrange fillets, skin sides up, in 1 layer on top of artichokes.
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17
Roast, uncovered, until fillets are just cooked through, about 9 minutes.
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18
Divide fish and artichokes among 4 plates using a spatula, reserving pan juices.
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19
Stir together remaining 2 tablespoons oil, remaining tablespoon lemon juice, tarragon, and reserved pan juices and drizzle over fish.
