Methods and apparatus for grasping a suture and cinching and/or locking a tissue anchor are provided. In one variation, a tube is provided having a lumen and a resilient member that obstructs the lumen. A grasper may be advanced coaxially through the lumen, such that it reversibly displaces the resilient member and extends beyond the lumen's outlet to engage suture of the tissue anchor. With suture engaged, the grasper may be withdrawn within the tube, such that the resilient member again obstructs the lumen of the tube. Continued retraction of the grasper relative to the tube and anchor may act to cinch the anchor via interaction between a cinching/locking mechanism of the anchor and the obstructing resilient member. In an alternative variation, a snare device is provided comprising a resilient wire loop that coacts with an element of the snare device or of the tissue anchor for grasping and cinching the tissue anchor.