The remora fishes are capable of adhering to a wide variety of natural and artificial marine substrates using a dorsal suction pad. The pad is made of serial parallel pectinated lamellae which are homologous to the dorsal fin elements of other fishes. Small tooth-like projections of mineralized tissue from the dorsal pad lamella, known as spinules, are thought to increase the remora's resistance to slippage and thereby enhance friction to maintain attachment to a moving host. In this work, the geometry of the spinules and host topology as determined by micro-computed tomography and confocal microscope data, respectively, are combined in a friction model to estimate the spinule contribution to shear resistance. Model results are validated with natural and artificially created spinules and compared to previous remora pull-off experiments. It was found that spinule geometry plays a critical role in friction enhancement especially at short spatial wavelengths in the host surface, and that spinule tip geometry is not correlated with lamellar position. Furthermore, comparisons with pull-off experiments suggest that spinules are primarily responsible for friction enhancement on rough host topologies such as shark skin