A patella drilling system includes a clamp and a patella drill guide. The clamp includes an arm with a pointed tip that is received in a dimple on the surface of the patella drill guide and another arm with a bone-gripping member spaced from the tip. The clamp is used to hold the patella drill guide firmly against the resected posterior surface of the patella while the surgeon drills into the patella to form holes for mounting pegs on the implant. The clamp may allow the patella drill guide to be pivoted while clamped so that the orientations of the guide bores may be optimized. The system includes an optional cap that may be used on the pointed tip of the clamp to hold the implant firmly in place while the bone cement sets.