Trim the stems, as necessary. Trim the points if you care to do so.
Parcook the artichokes until about halfway done, by steaming.
Remove the artichokes from the pot, and shock them. If you're planning on serving the artichokes as a side, and haven't trimmed them all the way down, cut them in half lengthwise, and remove the choke. If you're planning on ultimately pureeing the artichokes or serving as heart and stem chunks (salads, dips), "turn" the artichoke to remove everything inedible.
Either way, you may hold them in the refrigerator for up to several days.
Place the halved or turned artichokes in the smoker and smoke for about half an hour. Mesquite, oak, citrus, alder, grape cuttings, citrus -- best. Other fruitwoods, pecan, maple, very good. Hickory -- not a great choice, it's sweetness tends to make the artichoke taste weird.
Once they've taken on some smoke, finish cooking the halved artichokes to slightly charred limpness on the grill. Depending on the size of the artichokes and the smoker temperature, that probably won't take long at all. Serve as an "upscale barbecue" app or side, along with lemon, balsamic, aioli, or seasoned butter. However you sauce, think about working in some garlic.
As for the turned, smoked artichokes. Chunk and use for an artichoke/spinach dip, an omeletter, etc. Or, puree and use for a soup.
If you haven't tried smoked artichoke hearts fried in a parmesan tempura batter, well I just don't know what.
Many wines do not pair well with artichokes, which tends to make big reds especially taste sweet -- and not in the good way. Spicy whites like dry traminers do OK. Fumes too. Sangria, a definite yes. Some cocktails, like mojitos if they're not too sweet. Anything citrussy, ditto. Beer is probably A Number One, if the situation allows.