  Applications of the general theory of quantum electrodynamics with Lorentz-
and CPT-violating operators of mass dimensions up to six are presented to
Penning-trap experiments comparing charge-to-mass ratios between particles and
antiparticles. Perturbation theory is used to derive Lorentz- and CPT-violating
contributions to the energy levels and cyclotron frequencies of confined
particles and antiparticles. We show that whether the experimental {\it
interpreted} quantity $(|q|/m)_{\overline{w}}/(|q|/m)_{w} - 1$ is a clean
measure of a CPT test depends on the context of the relevant theory. Existing
experimental results of charge-to-mass ratio comparisons are used to obtain
first-time constraints on 69 coefficients for Lorentz and CPT violation.
