We get the small artichokes in a 4 pack from Trader-Joes, but you could use the large ones too. Start by trimming the spiky parts off with a pair of kitchen scissors. Next, slice them lengthwise and remove all the furry stuff on the inside. Mix together ½ cup olive oil, juice from 1 lemon, 3-4 crushed garlic cloves, and salt and pepper to taste. Set the artichoke halves on a plate and liberally apply the mixture on all sides using a basting brush.
Throw the artichokes on the grill 10 minutes before you remove the tri-tip. Cook for 10-15 minutes and flip occasionally so they get nicely charred. 5 minutes before removing make sure the artichokes are face up and baste them with the garlic/lemon mixture.