Fill a bowl with water and squeeze the juice of ½ lemon into the water.
Wash the artichokes and trim the spikes off the leaves. Cut each artichoke in half lengthwise and scoop or cut out the choke completely. Place artichokes in the lemon water so they don't brown.
Steam the artichokes over water and the juice of the other ½ of the lemon until fork-tender, approximately 20 minutes.
Preheat the oven to 375 degrees.
In a bowl, mix together the olive oil, balsamic vinegar, and garlic. Season with salt and pepper, to taste. Dip the steamed artichokes into the vinegar mixture, making sure to coat each side. Place the artichokes cut side down in a roasting pan. Pour the excess vinegar mixture over the artichokes.
Roast the artichokes in the oven for approximately 30 minutes. Remove from the oven and serve warm.