Light the grill, using only hardwood or lump charcoal. The fire is ready in approximately 20 minutes or when the coals glow red and white ash begins to appear on the coals. Spread the charcoal in a single layer to evenly distribute the heat. If you need to add additional coals at any time, arrange them around the rim and they will catch quickly without disturbing the glowing center coals. Set the grill rack 4 inches above the fire and let it heat for 5 minutes. The fire is ready for grilling when you can barely hold your hand 4 inches above the coals for 4 seconds. This is the test for a medium-hot fire.
Trim about 1 inch off the thick woody end of each asparagus spear; the younger and fresher the asparagus, the less you will need to trim from the bottom. Strip away the hard and stringy outer portion of the stalks with a sharp vegetable peeler. Arrange the asparagus in a shallow dish. Drizzle with the olive oil and turn to coat.
Sprinkle salt and a heavier portion of pepper on a plate and mix well. Roll each spear of asparagus in the salt mixture until lightly coated.
Arrange the spears on the grill rack. Grill for 10 minutes or until light brown and of the desired degree of tenderness, turning frequently. Place the asparagus in a shallow serving dish. Drizzle with a mixture of the orange juice and lemon juice. Serve hot or at room temperature. Garnish with strips of orange zest and lemon zest.