The document describes a method for designing and characterizing graphene-on-silicon waveguides. The waveguides consist of a silicon core covered by a thin graphene layer that matches the width of the silicon core. Simulations using OptiFDTD software showed that the graphene layer retained its properties after processing and the waveguides had lower propagation losses for transverse electric and magnetic modes than bare silicon waveguides. Measurements found the losses were higher for the TM mode than the TE mode. The method provides a simple way to integrate graphene with silicon photonics without requiring precise alignment of the graphene.