The invention is devices and techniques which use a negative (suction) pressure or vacuum, applied through a surgical instrument, to fix the position of a portion of the surface of a beating heart so that a surgical procedure can be more easily performed. The devices apply a negative pressure at several points on the outer surface of the heart such that a portion of the heart is fixed in place by the suction imposed through the surgical instrument. Because the instrument fixes the position of the tissue, and because the instruments remain at a constant distance from the particular portion of the heart where the surgery is being performed, the device may also serve as a support or platform so that other surgical instruments or devices can be advantageously used at the site. In certain preferred embodiments, the devices described herein have structures to facilitate the use of additional surgical instruments such that the placement of negative pressure device permit the surgeon to advantageously manipulate the other instruments during surgery. The negative pressure is preferably imposed through a plurality of ports which may be disposed in a substantially planar surface of the instrument which contacts the cardiac tissue.