Advances in three-dimensional nanofabrication techniques have enabled the development of lightweight solids, such as hollow nanolattices, having record values of specific stiffness and strength, albeit at low production throughput. At the length scales of the structural elements of these solids-which are often tens of nanometers or smaller-forces required for elastic deformation can be comparable to adhesive forces, rendering the possibility to tailor bulk mechanical properties based on the relative balance of these forces. Herein, we study this interplay via the mechanics of ultralight ceramic-coated carbon nanotube (CNT) structures. We show that ceramic-CNT foams surpass other architected nanomaterials in density-normalized strength and that, when the structures are designed to minimize internal adhesive interactions between CNTs, more than 97% of the strain after compression beyond densification is recovered. Via experiments and modeling, we study the dependence of the recovery and dissipation on the coating thickness, demonstrate that internal adhesive contacts impede recovery, and identify design guidelines for ultralight materials to have maximum recovery. The combination of high recovery and dissipation in ceramic-CNT foams may be useful in structural damping and shock absorption, and the general principles could be broadly applied to both architected and stochastic nanofoams.