Preheat oven to 375 degree Fahrenheit.
Remove tarragon leaves from the stems; place aside. Wash and dry kumquats; slice in half and remove all seeds; place aside. Crush, dice, or press the garlic cloves; place aside. Rinse game hens with cold water and pat dry.
Separate the skin from the game hen’s breast. Push in the tarragon leaves and crushed garlic under the skin; the skin protects the leaves and garlic from burning. Place tarragon stems inside the hen’s cavity, along with about 35-40 seeded kumquats.
Place game hens on a raised rack in a roasting pan. Add 1/2 cup of water to the bottom of the pan to prevent the juices from burning. Cook for about one and ½ hours at 375 degrees Fahrenheit. Baste frequently and replenish the water in the pan as needed.
Optional: Place giblets in a saucepan and cover with water. Cook over medium heat until done, about 1 hour. Remove and allow to cool. Chop and set aside.
Coarsely chop the remaining 10 to 15 kumquats. In a sauce pan, combine the orange juice, sugar, and kumquats. Bring to a slow boil and reduce heat to a low simmer. Stir frequently and cook until done, about 30 to 45 minutes. Set aside.
Remove the game hens from the oven after 90 minutes or when golden brown and done. Transfer the game hens to a serving platter. Remove and discard the tarragon stems. Reserve the cooked kumquats and decoratively place around the hens.
Deglaze the roasting pan and transfer the drippings to a saucepan. Carefully add the flour to make a roué. Add chicken broth and cook over medium heat until the gravy is thickened, about 5 to 10 minutes. Add giblets (optional).
Combine the orange liqueur with orange juice/kumquat sauce and add to gravy. Simmer another 5 minutes. Transfer to gravy boat.
Carve game hens and serve each portion with gravy and kumquats.