Disclosed herein are electromagnetic logging systems and methods that provide a set of signals that robustly approximate the response of a model tool employing orthogonal triads of point-dipole antennas. One illustrative method embodiment obtains an azimuthally sensitive electromagnetic logging tool's signal measurements as a function of position in a borehole, the tool having at least two spacing distances (d1, d2) between transmit and receive antennas. Orthogonal direct coupling measurements (Vxx, Vyy, Vzz) are derived from the signal measurements and converted into a set of robust signals, the set including: a ratio between Vzz coupling components at different spacing distances, a ratio between Vxx and Vzz coupling components, a ratio between Vyy and Vzz coupling components, and a ratio between Vxx and Vyy coupling components. The set may include an additional robust signal having a ratio between a sum of cross-coupling components Vxz+Vzx or Vyz+Vzy and a sum of orthogonal direct coupling components.