This paper presents a circuit-based self-consistent electrothermal model of Power Delivery Networks (PDNs) fabricated with carbon nanotubes, for nanoscale integrated circuits. It couples the electrical submodel with an equivalent circuit submodel of the thermal problem, and allows characterizing the PDNs in terms of both voltage drop and temperature rise. The temperature dependence of the PDNs electrical parameters is taken into account through physically meaningful models of the mean free path and the number of conducting channels in carbon nanotubes. The model is used to compare the performance of conventional copper PDNs with those of PDNs realized with bundles of carbon nanotubes in different configurations (single-wall, multiwall, and mixed). The adopted values of thermal and electrical parameters are those typically obtainable with the current fabrication processes, for technology nodes of 65 and 22 nm and different core power consumption.