Where the magnetic permeability of rock or soil exceeds that of free space, the effect on airborne electromagnetic systems is to produce a frequency‐independent shift in the in‐phase response of the system while altering the quadrature response only slightly. The magnitude of the in‐phase shift increases as (1) the relative magnetic permeability is increased, (2) the amount of magnetic material is increased, and (3) the airborne sensor gets nearer the earth’s surface. Over resistive, magnetic ground, the shift may be evinced by negative in‐phase measurements at low frequencies; but over more conductive ground, the same shift may go unnoticed because of the large positive in‐phase response. If the airborne sensor is flown at low levels, the magnitude of the shift may be large enough to affect automatic inversion routines that do not take this shift into account, producing inaccurate estimated resistivities, usually overestimates. However, layered‐earth inversion algorithms that incorporate magnetic permeability as an additional inversion parameter may improve the resistivity estimates. We demonstrate this improvement using data collected over hazardous waste sites near Oak Ridge, Tennessee, USA. Using resistivity inversion without magnetic permeability, the waste sites are almost invisible to the sensors. When magnetic permeability is included as an inversion parameter, the sites are detected, both by improved resistivity estimates and by estimated magnetic permeability.