A simple model of an internal wave advected by an oscillating barotropic flow suggests flaws in standard approaches to estimating properties of the internal tide. When the M2 barotropic tidal current amplitude is of similar size to the phase speed of the M2 baroclinic tide, spectral and harmonic analysis techniques lead to erroneous estimates of the amplitude, phase, and energy in the M2 internal tide. In general, harmonic fits and bandpass or low-pass filters that attempt to isolate the lowest M2 harmonic significantly underestimate the strength of M2 baroclinic energy fluxes in shelf seas. Baroclinic energy flux estimates may show artificial spatial variability, giving the illusion of sources and sinks of energy where none are actually present. Analysis of previously published estimates of baroclinic energy fluxes in the Celtic Sea suggests this mechanism may lead to values being 25%–60% too low.