Honeycomb cores are used extensively in different sectors of industry to build advanced lightweight structures which take advantage of high stiffness-to-weight and strength-to-weight ratios. To further increase their mechanical properties, structural hierarchy is considered already from a conceptual point of view. It is proven to be highly effective in enhancing mechanical performance in different loading scenarios but affordable realisation of practical applications remains limited. The present study focuses on the out-of-plane compressive behaviour of a novel hierarchical sandwich honeycomb core with an emphasis on compressive strength, both in virtual and in experimental testing. The finite element model is validated for through-the-thickness compressive loading by physical experiments and it can subsequently be used for further structural optimization. The paper concludes with a comparison between the proposed hierarchical structure and conventional expanded honeycombs. The performance analysis highlights the advantages of the introduction of structural hierarchy to the state-of-the art honeycomb and it shows a high potential for the use in the construction of sandwich panels and parts.