Hunh. My recipe seems to have disappeared. It was originally from barbecue-online.co.uk
Basically, you marinate the artichokes in lemon juice, tarragon, salt, and olive oil for x number of hours. I wrap them in foil and toss 'em on the grill, main grate. Add a garlic-orange juice mayonnaise, and voila!
I've also been known to steam them and serve them with hollandaise sauce, which is how I grew up with them.