Mechanical metamaterials, a novel class of cellular solids, have recently received much attention since they provide an innovative path to the realization of materials with both low density and high stiffness. They typically have carefully designed periodic structures, often at the micro/nano-scale, which lead to unique mechanical properties defined by their architecture. Past research in mechanical metamaterials has concentrated on the architecture (e.g. bending-dominated and stretching-dominated), fabrication techniques (e.g. self-propagating photopolymer waveguide, direct write lithography and printing, and self-assembly) and mechanical characterizations (e.g. stiffness, strength, and recoverability) of three-dimensional truss-like bulk mechanical metamaterials. The underlying material of previously reported mechanical metamaterials typically created an interconnected periodic structure which could be easily penetrated by gas. In contrast, we recently proposed the concept of plate mechanical metamaterials, which are cellular plates with carefully engineered and tightly controlled periodic architectures. Standard micro/nano-fabrication processes were developed to fabricate ultra-lightweight, stiff, robust, flat and scalable single/two-layer continuous plates and nanocardboard hollow sandwich plates out of ultrathin insulating alumina films formed by atomic layer deposition. These standard optical lithography based fabrication techniques enable the mass production of these plate mechanical metamaterials by allowing nearly arbitrary in-plane geometry. Similar to the shape-recovering property of bulk mechanical metamaterials under large shear or compression deformations, the plate mechanical metamaterials could recover their original shapes after extreme bending deformations, which is explained by the elastic shell buckling of ultrathin features. A nanocardboard sandwich plate—the analog of corrugated cardboard with nanoscale plate thickness, microscale plate height and macroscale lateral dimensions—was first fabricated. Nanocardboard can achieve the highest ratio of bending stiffness to areal density, outperforming all other reported materials. These plate mechanical metamaterials can be used in many fields, such as serving as the standoffs in high-efficiency thermionic energy converters. The thermal and mechanical properties of the standoffs were characterized, showing excellent thermal insulation and mechanical robustness. The experimental thermal resistance of standoffs had no obvious dependence on plate thickness or inter-electrode gap distance, and generally decreased with out-of-plane apparent applied pressure.