A method for making downhole electromagnetic logging while drilling measurements includes rotating an electromagnetic logging while drilling tool in a subterranean wellbore. The logging while drilling tool includes at least first and second tilted transmitter antennas longitudinally spaced along a logging while drilling tool body and at least first and second tilted receiver antennas. A plurality of electromagnetic voltage measurements is acquired at the first and second tilted receiver antennas while rotating and processed to compute harmonic voltage coefficient. Ratios of selected ones of the harmonic voltage coefficients are then processed to compute at least one gain compensated measurement quantity.