The work presented in this thesis is designed to demonstrate the value and capacities of TESS to contribute to asteroseismology of compact pulsators. I find that TESS data are able to reproduce some of the results obtained by the ground by collaborations like the Whole Earth Telescope (WET) given its ability to observe a star nearly continuously for approximately 27 days. I also address some of the weaknesses of the TESS observations for these purposes, such as the CCD pixel size on the TESS cameras, long integration times, and the bandpass of the telescope's detector. I examined four white dwarf pulsators and found that the MCT 0145-2211 and HE 0532-5605 lack long lifetime modes of pulsation. I place upper limits on the amplitudes of any pulsations in the TESS bandpass. The hottest of the pulsators studied, ZZ Ceti, appeared as expected (after accounting for the TESS bandpass) based on the many ground-based observations of the star. Ultimately the results of this work demonstrate the value of TESS as the next step forward in the field of asteroseismology.