Recent experimental achievements of conductance measurements through single molecules have initiated novel research directions in the solid state physics at the nanometer scale, with molecular electronics as a forefront. Apart from its great potential for applied and industrial research, molecular electronics also poses a wealth of challenges to basic research. Direct efforts are needed to comprehend the conduction mechanisms in molecular and supramolecular systems. One of the main issues deserving more intense investigations is the role of the coupling between molecules and nanoleads in contrast to the usually adopted bulky electrodes. On the other hand studies on the electronic properties of carbon nanotubes suggest their promising utilization as wiring elements of molecular circuits. Therefore, we address the problem of electron transport across a system consisting of a molecular wire attached to two semi-infinite carbon nanotubes. Within the Landauer scattering matrix approach combined with a recursive Green function technique for tight binding electrons, we obtain the conductance as a function of system parameters such as the coupling strength, and the contact geometry. The conductance exhibits markedly different behaviors for the two limiting scenarios of a single contact and a multiple contact between the wire and the nanotube interfacial atoms. In particular, the latter configuration supports a single channel transport, exhibits a scaling law for the conductance as a function of the coupling strength and tube diameter, and manifests a counter intuitive enhancement of the conductance when the coupling becomes weaker.