``Action and phase jump'' analysis is presented---a beam based method that uses amplitude and phase knowledge of a particle trajectory to locate and measure magnetic errors in an accelerator lattice. The expected performance of the method is first tested using single-particle simulations in the optical lattice of the Relativistic Heavy Ion Collider (RHIC). Such simulations predict that under ideal conditions typical quadrupole errors can be estimated within an uncertainty of 0.04%. Other simulations suggest that sextupole errors can be estimated within a 3% uncertainty. Then the action and phase jump analysis is applied to real RHIC orbits with known quadrupole errors, and to real Super Proton Synchrotron (SPS) orbits with known sextupole errors. It is possible to estimate the strength of a skew quadrupole error from measured RHIC orbits within a 1.2% uncertainty, and to estimate the strength of a strong sextupole component from the measured SPS orbits within a 7% uncertainty.