Precision experiments with muons are sensitive to Planck-scale CPT and Lore
ntz violation that is undetectable in other tests. Existing data on the muo
nium ground-state hyperfine structure and on the muon anomalous magnetic mo
ment could be analyzed to provide dimensionless figures of merit for CPT an
d Lorentz violation at the levels of 4 X 10(-21) and 10(-23).