Corrugated paper cardboard provides an everyday example of a lightweight, yet rigid, sandwich structure. Here we present nanocardboard, a monolithic plate mechanical metamaterial composed of nanometer-thickness (25-400 nm) face sheets that are connected by micrometer-height tubular webbing. We fabricate nanocardboard plates of up to 1 centimeter-square size, which exhibit an enhanced bending stiffness at ultralow mass of ~1 g m-2. The nanoscale thickness allows the plates to completely recover their shape after sharp bending even when the radius of curvature is comparable to the plate height. Optimally chosen geometry enhances the bending stiffness and spring constant by more than four orders of magnitude in comparison to solid plates with the same mass, far exceeding the enhancement factors previously demonstrated at both the macroscale and nanoscale. Nanocardboard may find applications as a structural component for wings of microflyers or interstellar lightsails, scanning probe cantilevers, and other microscopic and macroscopic systems.