Creating lightweight, mechanically robust materials has long been an engineering pursuit. Many siliceous skeleton species--such as diatoms, sea sponges and radiolarians--have remarkably high strengths when compared with man-made materials of the same composition, yet are able to remain lightweight and porous. It has been suggested that these properties arise from the hierarchical arrangement of different structural elements at their relevant length scales. Here, we report the fabrication of hollow ceramic scaffolds that mimic the length scales and hierarchy of biological materials. The constituent solids attain tensile strengths of 1.75 GPa without failure even after multiple deformation cycles, as revealed by in situ nanomechanical experiments and finite-element analysis. We discuss the high strength and lack of failure in terms of stress concentrators at surface imperfections and of local stresses within the microstructural landscape. Our findings suggest that the hierarchical design principles offered by hard biological organisms can be applied to create damage-tolerant lightweight engineering materials.