Remove and discard giblet, if any. Rinse hens inside and out and pat dry. Loosen skin from the breasts and place hens in a large resealable plastic bag.
Whisk orange juice, orange zest, tarragon, garlic, mustard, salt, and pepper together in a small bowl. Whisking continually, slowly drizzle in olive oil until combined. Pour marinade over the hens in the bag, making sure to get some under the skin. Seal bag and refrigerate at least 1 hour.
Preheat the oven to 450 degrees F (230 degrees C).
Remove hens from the bag, letting excess marinade drip off; pour remaining marinade into a small saucepan and set aside. Place hens in a small roasting pan and season with salt and pepper. Tie legs together with kitchen twine and tuck wing tips underneath.
Roast in the preheated oven for 20 minutes. Reduce heat to 350 degrees F (175 degrees C). Continue cooking, basting with pan juices every 10 to 15 minutes, until hens are golden brown and internal temperature reaches 165 degrees F (74 degrees C), 25 to 30 minutes more.
Transfer hens to a serving plate, pouring any cavity juices back into the roasting pan. Tent with aluminum foil and keep warm.
Scrape pan juices and pour through a strainer into the saucepan with the reserved marinade. Bring to a boil and simmer 5 minutes, whisking occasionally. Season sauce with salt and pepper, if necessary.
Serve Cornish hens whole or cut in half. Spoon pan sauce over hens to serve.
