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Preheat the oven to 325 degrees F
To begin the stew: Remove the hens from the marinade and blot them dry with paper towels. Strain the marinade into a bowl and reserve. Reserve the vegetables separately.
Heat the oil in a heavy casserole over medium-high heat. Working in batches, brown the Cornish hens on all sides, about 15 minutes per batch. Set the browned birds aside and add the reserved marinated vegetables to the pot. Turn the vegetables once or twice in the oil then sprinkle them with the flour. Cook, stirring frequently until the flour smells toasted, about 3 minutes, then add the reserved marinade. Bring the marinade to a boil. Reduce the heat to medium-low. Return the Cornish hens to the pot, cover, and braise in the oven until the hens are well-cooked, about 45 minutes.
Meanwhile, prepare the vegetables. Bring a large pot of salted water to a boil over high heat. Cook the onions until they are just tender, about 7 minutes, then remove them with a slotted spoon. Add the celery to the pot and cook until it too is tender, about 3 minutes. Refresh the celery in ice water. Set the celery and onions aside.
Finishing the stew: When the Cornish hens are ready, transfer them to a serving plate and remove the toothpicks or string.
Strain the braising liquid through a fine sieve. Pour the strained liquid into a large skillet and warm over low heat. Stir in the port, the red currant jelly and the cream. Keep the sauce warm over low heat.
To serve, spoon sauce over the Cornish hens then surround with glazed vegetables.