In recent years, there has been much interest in modelling graphene nanoribbons as they have great potential for use in molecular electronics. We have employed the NEGF formalism to determine the conductivity of graphene nanoribbons in various configurations. The electronic structure calculations were performed within the framework of the Extended Huckel Approximation. Both zigzag and armchair nanoribbons have been considered. In addition, we have also computed the transmission and conductance using the non-equilibrium Greens function formalism for these structures. We also investigated the effect of defects by considering a zigzag nanoribbon with six carbon atoms removed. Finally, the effect of embedding boron nitride aromatic molecules in the nanoribbon has been considered. The results of our calculations are compared with that obtained from recent work carried out using tight-binding model Hamiltonians.