WC/amorphous carbon (a-C) thin films were deposited by dual magnetron sputtering from individual WC and graphite targets. The influence of film composition and microstructure on the optical and electrical properties was investigated. As evidenced by x-ray photoelectron spectroscopy and grazing angle x-ray diffraction measurements, the WC/a-C films are composite materials made of hexagonal W2C and/or cubic beta-WC1-X nanocrystallites embedded in (a-C) matrix. The optical properties were studied by spectroscopic ellipsometry and the electrical resistivity was measured by the van der Pauw method between 20 and 300 K. Both the optical and the electrical properties of the WC/a-C films are correlated with the chemical composition and microstructure evolution caused by a-C addition. The optical properties of W2C/a-C and beta-WC1-x/a-C films with a-C content <= 10 at. % are explained by modeling their dielectric functions by a set of Drude-Lorentz oscillators. Further increase in a-C content leads only to the formation of beta-WC1-x/a-C nanocomposite structures and their optical properties progressively evolve to those of a-C single phase. The electrical resistivity as a function of the temperature of all the films exhibits a negative temperature coefficient of resistivity. Theoretical fitting using the grain-boundary scattering model shows that the transport properties are mainly limited by the grain size and electron mean free path parameters.