The present invention provides a vibration damping mount with which a vibration damping action is improved and also provides a metal heat shield with which a sound insulation performance is improved. The vibration damping mount includes: a substantially annular damping member that has an insertion hole, through which the bolt to be attached to an attachment boss is inserted, and externally surrounds the bolt; a grommet that includes a first retaining section for retaining a heat shield, a second retaining section for retaining the damping member, and a coupling section for coupling the first retaining section and the second retaining section, the second retaining section, the coupling section, and the first retaining section being provided in this order from the attachment boss side; and a collar member that includes a pair of flange sections, which nip the damping member from both sides in an axial direction with gaps formed on both the sides, and a coupling section, which couples the pair of flange sections each other and has a gap in a radial direction between the coupling section and the damping member.