  Precision experiments with muons are sensitive to Planck-scale CPT and
Lorentz violation that is undetectable in other tests. Existing data on the
muonium ground-state hyperfine structure and on the muon anomalous magnetic
moment could be analyzed to provide dimensionless figures of merit for CPT and
Lorentz violation at the levels of $4\times 10^{-21}$ and $10^{-23}$.
