Heat the ridged grill pan or barbecue to medium. Trim the outer layers of leaves and tops carefully off the fennel bulbs (do not discard these, but wrap and freeze, they can be used to good effect in fish broths and soups). Shave the base of the fennel with a potato peeler to clean it; you want the base to hold the leaves together, so do not cut. Divide the fennel bulbs into quarters longitudinally, using a sharp knife, but be careful or the quarters will break up into separate layers.
Grill the fennel quarters for approximately 5 minutes on each flat face and 5 minutes on the rounded outer side. Do not play with them, but leave alone until it is time to turn. Serve warm or at room temperature, having adjusted the seasoning. Offer oil and lemon juice.