A surgical stabilizer for use with a surgical site retractor has a base, a bendable arm, and a distal cuff adapted to resiliently hold a tube of an elongated port-access device. The cuff may have a body defining a partial enclosure within which is held a highly flexible gasket having a slit for resiliently receiving the tube. The surgical site retractor may have a collapsible ring and a flexible outer portion attached thereto, the ring being sized to pass through an intercostal incision and expand therein under adjacent ribs to prevent removal, and the flexible outer portion extending out of the incision and drawing over the stabilizer base to mutually secure the retractor and base. The port-access tube may be for a heart valve delivery system using an elongated port-access device for transapically delivering a prosthetic heart valve to the aortic valve annulus. A method involves partly installing the surgical site retractor, anchoring the base of the stabilizer with the flexible outer portion, deploying the port-access tube from outside the body through the incision and through a puncture in the heart wall, and resiliently capturing a tube of the port-access within the partial enclosure of the stabilizer cuff. A second bendable arm on the base having a clip may be used to hold still a proximal end of the port-access device.