  We calculate complex-temperature (CT) zeros of the partition function for the
$q$-state Potts model on the honeycomb and kagom\'e lattices for several values
of $q$. These give information on the CT phase diagrams. A comparison of
results obtained for different boundary conditions and a discussion of some CT
singularities are given. Among other results, our findings show that the Potts
antiferromagnet with $q=4$ and $q=5$ on the kagom\'e lattice has no phase
transition at either finite or zero temperature.
