A few years ago I created a Margarita Shrimp recipe that's perfect for Maine shrimp. It's peel-and-eat and at it's very best if you find the shrimp with heads on. You can make it with other shrimp -- you just saute it longer.
You make a margarita, cut up scallions and saute them in butter & olive oil, add the margarita, when it bubbles add the shrimp and saute for a minute add pepper and serve with lime wedges.
More detail and photos here.
The Belgian's have a similar shrimp (Grey shrimp, even smaller!) that they cherish and use in different ways. I have done both the following recipes with maine shrimp and both worked very well.
The simple one is Crevette aux Tomate: Shrimp stuffed into Tomatoes. Maybe not a good time this season, but what they do is:
Poach the shrimp in court bouillion, but never boil. Just bring up to a near boil and remove. peel.
Mix with homemade mayo (ok, or Helman's), chives. lemon, salt and pepper and place, overflowing, in a good cored-out tomato. Simple, but great.
The other is croquette de crevette, which is a fantastic roux based croquette (fritter?) that is a little complicated, but is considered a high delicacy in Belgium. When you cut into it it oozes briney, sweet, shrimpy goodness. My wife's grandmother taught it to me and I would be happy to explain it if you want.
Raw with very high quality olive oil, lemon salt and pepper. Possibly barely cooked with citrus juice in a ceviche. Do NOT overcook them, they are soo sweet and delicious and will dry out very quickly. If you need to cook them, saute them in a hot skillet for 30 - 45 secs at most maybe some garlic, parsley, o.o. s&p. Keep it simple or you won't be able to taste the shrimp and their inherent sweetness.