A septal occlusion device for closing an abnormal opening in the heart includes a wire mesh support structure with a first disk, a second disk, and a waist portion joining the first and second disk; and a thin-film micromesh coupled to the wire mesh and configured to extend across the abnormal opening. A left arterial appendage (LAA) occlusion device for sealing an LAA in the heart includes a support structure having a plurality of struts extending radially from a center to a distal portion to form a substantially hemisphere or dome shape, the distal portion of each strut being configured to engage an interior wall of the left arterial appendage, and a thin-film micromesh cover attached to the support structure and configured to extend across the opening of the left arterial appendage.