Put a skillet on at medium high with about 3 tbsp. of olive oil. Take your game hen (or chicken) and with a pair of kitchen scissors cut the back bone out by cutting down each side of it .Open it up and split the inside of breast bone with a sharp knife and spread it out flat. Salt and pepper both sides and put it in the pan skin side down. When the skin has browned turn it over and do the other side for a few minutes until it has started to brown.
While the chicken is browning slice up two limes chop up 4 garlic cloves and trim the leaves off a bunch of cilantro.Remove the hen to a plate and put the cilantro, garlic and limes in the pan. Add the white wine and sprinkle a little salt and pepper.
Put the hen and the drippings back in the pan. reduce the heat to medium low and cover the pan. Let it cook for about a half hour to 45 minutes. t's done when you can split the meat off the thigh bone and there is no trace of red or pink near nor on the bone. Or, a meat thermometer should read 165°F when inserted into the meatiest part of the thigh without touching the bone.
When the hen is done remove it to a plate and increase the heat to medium high. Let the liquid reduce a little and use it as a sauce on top of the servings the hen.