The understanding of the electronic systems of materials has not been only the essential, but the driving force, behind the progress of technology for over 100 years. This year marks the 60th anniversary of the revolutionary Bardeen-Cooper-Schrieffer, or BCS, theory which described the creation of Cooper pairs from a Fermi liquid ‘normal’ state through a coupling of conduction elections to phonons. Despite this, it wasn’t until the cuprate La2−xBaxCuO4, the first high-temperature superconductor, was discovered in the late 1980’s  that the dream of a room temperature superconductor seemed attainable and the ‘Age of the Superconductor’ began. However, the unique properties for which these high-temperature, unconventional superconductors are prized have also obstructed thorough investigation of the electronic behavior underlying their superconductivity and demanded extremely intense magnetic fields, very low temperatures, and thermodynamic measurements in extreme environments in order to fully characterize their electronic systems. It is, therefore, no small thing to flesh out the phase diagrams of these materials whose exotic electronic properties may eventually lead to faster, more compact devices and new methods of digital computation. Despite the difficulties in collecting usefully data on high-temperature superconductors, a vast body of work has amassed and grown with the increasingly intense magnetic fields available. As a result, quasiparticle mass enhancement near optimal doping was recently observed in two major classes of high-temperature superconductors, cuprates  and pnictides [3–5]. Because an effective quasiparticle mass accounts for the interactions between an electron and surrounding particles, it is an experimental indicator of enhanced electronic interactions. Enhancement of the quasiparticle effective mass, or increased electronic interactions, is believed to accompany quantum criticality, and the observation of mass enhancement in two very different classes of high-temperature superconductors makes quantum criticality the most promising candidate for universality across the high-temperature superconductors. The study outlined here is an investigation of the properties of three high-temperature superconductors, La2−xSrxCuO4, YBa2Cu3Oδ , and BaFe2(As1−xPx)2, through specific heat and resistivity measurements at very low temperatures, 1.5 K ≤ T ≤ 20 K, and magnetic fields up to 35 T. Such measurements required the construction of instrumentation specifically designed to deal with these extreme environments, and the low thermodynamic signals which are a signature of the cuprate superconductors. In order to understand the unprecedented data collected, novel analysis techniques based on Volovik phenomenology were developed. The procedures for specific heat measurements and the analysis of the resulting data developed for this study and outlined in the following thesis stand as the model for measurement of the normal state density of states of correlated superconductors. I report the observation of a saturation of the specific heat as a function of applied magnetic field in all three compounds, La2−xSrxCuO4, YBa2Cu3Oδ , and BaFe2(As1−xPx)2, indicating superconductivity has been suppressed and from which an effective mass, or sum of quasiparticle masses can be determined. I report that the onset of the normal state corresponds to the onset of finite resistance in La2−xSrxCuO4 and BaFe2(As1−xPx)2. I report enhancement in the sum of quasiparticle masses with doping in BaFe2(As1−xPx)2 that diverges near the predicted quantum critical point at optimum doping and that the dramatic enhancement evidences an orbital selective coupling to quantum fluctuations when compared to previous studies.