This study investigates the possibility of electromagnetic heating of carbon fibre composites (CFCs) to the resin curing temperature, utilising Joule heating, with the main potential application being the on-site and in-situ repair of damaged CFCs. The study describes the energy conversion from the supplied AC electrical current to the power generated and hence, heat produced in a CFC. This is investigated through the development of three-dimensional (3D) finite-element multiphysics models using a homogenous representation approach, which can represent single- and multi-layer CFC lay-ups. An experimental test-rig is used to validate the 3D finite-element models for both unidirectional and quasi-isotropic CFCs. Both the numerical simulations and experimental results are in good agreement. The presented results show that electromagnetic induced Joule heating can be used to achieve resin curing temperatures in CFCs for potential applications such as in-situ repair.