Low-temperature series have been derived for the q-state Potts model on the Kagomé lattice (q = 3 and 4) and for the 3-state honeycomb lattice. The series are derived by the finite-lattice method, with many additional terms obtained by noting the structure of the correction terms. Accurate estimates of the critical points are found, which confirm exact, but not rigorous results in the case of the honeycomb lattice, and refute previous conjectures in the case of the Kagomé lattice.