A method for endovascularly replacing a heart valve of a patient. In some embodiments the method includes the steps of: endovascularly delivering a replacement valve and an expandable anchor in an unexpanded configuration within a catheter to a vicinity of the heart valve; deploying the anchor from the catheter; expanding the anchor to contact tissue at an anchor site; and retrieving the anchor into the catheter. The invention also includes an apparatus for endovascularly replacing a heart valve, including: a catheter; a replacement valve configured to be disposed within the catheter for delivery to a vicinity of the heart valve; and an expandable anchor configured to be disposed within the catheter for delivery to a vicinity of the heart valve, to be deployed from the catheter, to be expanded to contact tissue at an anchor site and to be retrieved back into the catheter after having been expanded.