Molecular dynamics simulations are reported for the pullout force and interfacial friction of single-and multiwall carbon nanotubes (CNT) with interwall sp(3) bonds embedded in a diamond matrix. The van der Waals interaction and sp(3) bonding are shown to have a strong influence on friction at the nano-scale interface. Multiwall CNTs (MWCNTs) with interwall sp(3) bonding have friction stresses two times larger than either single-wall CNTs (SWCNTs) or double-wall CNTs with no sp(3) bonding for the same nominal conditions. The friction stress follows the form tau = tau(0) + mu p, where mu is a friction coefficient and p the radial pressure. The measured p compares reasonably well to estimates based on the van der Waals interaction, and we find that the MWCNTs with interwall bonding have a larger friction coefficient mu. The origin of the higher friction is postulated to arise from increased interface roughness associated with the interwall bonding. Because higher interface friction is beneficial to composite strength and toughness, nanoceramic composites composed of MWCNTs could have improved properties as compared with SWCNTs for the same fundamental interface chemistry and composite structure.