Bring a large pot of lightly salted water to a boil. Place the lobster tails, flesh side up, in a single layer in a shallow baking dish. Brush with the melted butter; drizzle with the lemon juice. Set an oven rack 6" beneath the broiler. Preheat the broiler.
Cook the linguini in the boiling water until just tender. Meanwhile, place the wine, saffron, garlic and tarragon in a skillet and set over medium-high heat. Bring the mixture to a simmer and reduce the wine by half. Add the cream, salt and pepper, return to a simmer, and cook until a lightly thickened sauce forms, about 3 to 4 minutes. While the sauce simmers, broil the lobster tails until just cooked through, about 3 to 4 minutes; turn off the broiler and keep the lobster warm in the oven.
When the pasta is cooked, drain well, reserving 1/4 cup of its cooking liquid. Add the linguini and reserved cooking liquid to the sauce and toss to combine. Divide the linguini among pasta bowls. Arrange the half lobster tails on top. Garnish with the tarragon sprigs and serve.