  A theoretical analysis is performed of Penning-trap experiments comparing
protons and antiprotons to test CPT and Lorentz symmetry through measurements
of anomalous magnetic moments and charge-to-mass ratios. Possible CPT and
Lorentz violations arising at a fundamental level are treated in the context of
a general extension of the standard model of particle physics and its
restriction to quantum electrodynamics. In a suggested experiment measuring
anomaly frequencies a bound on CPT violation of 10^{-23} for a relevant figure
of merit is attainable. Experiments comparing cyclotron frequencies are
sensitive within this theoretical framework to different kinds of Lorentz
violation that preserve CPT. Constraints could be obtained on one figure of
merit at 10^{-24} and on another in a related experiment with H- ions and
antiprotons at the level of 10^{-25}.
