Planetary nebulae (PNs) that evolve from relatively high mass progenitor stars can "masquerade" as low-mass objects. We demonstrate this by simulating the evolution of PNs and their central stars based on simple models and by examining nebulae possessing a variety of wind speeds and mass-loss rates. We find that even when nebulae become ionized beyond the dense inner "snow-plowed" shell that forms, a faint ionized halo can comprise the great majority of ionized matter while contributing only a small fraction of the total luminosity of the nebula. For such a PN, standard techniques will severely underestimate the ionized mass. In other circumstances, standard assumptions about the nebular filling factor can cause an overestimation of the true mass.Curiously, the nominal ionized mass that would be derived for our model nebulae by standard methods (which we dub the "Shklovsky mass") proves to be relatively insensitive to variations in the input parameters of our simulations. After the PN is more than a few thousand years old, the Shklovsky mass consistently remains on the order of a few tenths of a solar mass, even though the total ionized mass varies between being slightly smaller to two orders of magnitude larger in some of our simulations. We show that the Shklovsky masses we derive are consistent with the range of masses that have been determined for PNs with independent distance estimates. The intrinsic scatter of the Shklovsky mass in our models would produce only ∼30% (1 σ) distance errors using the Shklovsky distance method. The small variance of the observed "Shklovsky mass" may explain why the Shklovsky distance method has been successful despite the apparent errors in its basic assumptions.