Bring a small amount of salted water to a boil in a pot with a steamer basket or insert. Steam the artichokes, adding more water to the pot if needed, until they are tender, 20 to 25 minutes.
Preheat a grill to high heat.
Transfer 2 artichoke halves to each of 6 large pieces of aluminum foil, drizzle the artichokes with a splash of melted butter and fold each piece of foil into a packet.
Grill for a minute or so over direct heat or for a bit longer over indirect heat. Serve with melted butter in dipping containers with some lemon juice squeezed into each. Eat with your hands and a roll of paper towels.