retrograde delivery catheter includes at its distal end a balloon configured to occlude the coronary sinus of a patient's heart, and has a length and flexibility which allow the distal end to be positioned in the coronary sinus with the proximal end extending transluminally to a peripheral vein such as an internal jugular vein and out of the body through a puncture therein. The delivery catheter has a delivery lumen extending between its proximal and distal ends which is configured to allow a cardioplegic fluid to be delivered at a flow rate of at least 200 ml/min with a pump pressure less than 300 mm Hg, thereby allowing cardioplegic arrest to be maintained using a blood cardioplegic fluid without causing excessive hemolysis. In a method of inducing cardioplegic arrest according to the invention, the patient is placed on cardiopulmonary bypass, the coronary arteries are isolated from remainder of the arterial system, and the delivery catheter is positioned transluminally in the coronary sinus from a peripheral vein. A cardioplegic fluid is then delivered to the coronary sinus through the delivery catheter at a flow rate of at least 200 ml/min and a pump pressure less than 300 mm Hg. The heart may be vented by withdrawing blood from the pulmonary artery through a catheter introduced through a peripheral vein, or withdrawing blood from the aortic root through an aortic catheter introduced through a peripheral artery.