Understanding the interaction of biological molecules with materials is essential in view of the novel potential applications arising when these two are combined. To this end, we investigate the interaction of DNA with diamondoids, a broad family of tiny hydrogen-terminated diamond clusters with high technological potential. We model this interaction through quantum-mechanical computer simulations and focus on the hydrogen bonding possibilities of the different DNA nucleobases to the lower amine-modified diamondoids with respect to their relative distance and orientation. Our aim is to promote the binding between these two units, and probe this through the association energy, the electronic structure of the nucleobase-diamondoid system, and the specific role of their frontier orbitals. We discuss the relevance of our results in view of biosensing applications and specifically nanopore sequencing of DNA.