Methods of deploying knotless suture locking clamps for securing prostheses such as heart valves or annuloplasty rings to facilitate implantation. The clamps have opposed clamp halves separated by a slot opening to one side and surrounded by a biasing member such as one or more C-clip springs. Sutures pass laterally into the slot which is held open by a retention member positioned between the clamp halves. The locking clamp slides along the sutures into position, the tension of the sutures is adjusted, and the retention member removed to allow the biasing member to clamp the sutures between the clamp halves. A delivery tool used to deliver and deploy the locking clamps contains a number of clamps within a delivery tube in a stack and bonded together for safety and a common retention member. The tool has a longitudinal channel on one side for entry of sutures.