This paper presents a performance analysis of Power Delivery Networks (PDNs) with innovative carbon-based materials, such as carbon nanotubes and graphene nanoribbons. The electrical and thermal performances of such PDNs are described in terms of voltage drop and temperature rise, respectively. The performance analysis is carried out by efficiently solving an electrothermal model, where the electrical and thermal sub-models are coupled in a relaxation approach. Compared to existing studies, a more accurate model for the electrical resistance of CNT or GNR interconnect is here introduced, allowing a more realistic description of the contact resistance and its dependence on the temperature. As a case study, a typical PDN structure for a chip at the 22 nm technology node is considered, and the results are compared to those obtained by using conventional conductors.