Pinch devices and access systems that can be used to secure a prosthetic heart valve to a heart valve annulus and to treat valvular insufficiency. A pinch device can be a separate expandable element from the prosthetic heart valve that is first advanced to the annulus and deployed, after which an expandable prosthetic heart valve can be advanced to within the annulus and deployed. The two elements can clamp/pinch the heart valve leaflets to hold the prosthetic heart valve in place. The pinch device can have a flexible, expandable annular frame. A combined delivery system can deliver the pinch device and prosthetic heart valve with just a single access point and aid more accurate coaxial deployment. The pinch device can be mounted near distal end of an access sheath, and a catheter for delivering the prosthetic heart valve can be passed through a lumen of the same access sheath.