A method of delivering a prosthetic mitral valve includes delivering a distal anchor from a delivery sheath such that the distal anchor self-expands inside a first heart chamber on a first side of the mitral valve annulus, pulling proximally on the distal anchor such that the distal anchor self-aligns within the mitral valve annulus and the distal anchor rests against tissue of the ventricular heart chamber, and delivering a proximal anchor from the delivery sheath to a second heart chamber on a second side of the mitral valve annulus such that the proximal anchor self-expands and moves towards the distal anchor to rest against tissue of the second heart chamber. The self-expansion of the proximal anchor captures tissue of the mitral valve annulus therebetween.