The co-integration between dielectric waveguides and graphene can open the way to the realization of photonic devices characterized by the well-established properties of mature technologies and by novel functionalities, e.g., the ultrafast tunability of the optical properties, that are typical of graphene-based devices. In this context, numerical modeling plays a key role. Graphene is often modeled as a thin layer with atomic thickness that is immersed in a micrometer-size dielectric structure, therefore the computational burden can become huge due to the size mismatch between the graphene layers and the environment. Here we demonstrate that the application of semi–analytical procedures based on the reformulation of techniques borrowed from classical optical waveguide theory allows to efficiently evaluate the modal properties of graphene–assisted dielectric waveguides. We consider two cases of study: first, we analyze an electro-absorption modulator based on the tunability of the conductivity of graphene. Then, a nonlinear waveguide where we exploit the huge third-order nonlinearity of graphene is studied. The excellent agreement between full-wave simulations and results obtained by applying the variation theorem for dielectric waveguides demonstrates the effectiveness of the approach.