We have designed a spectrometer for the quantitative determination of electron paramagnetic resonance (EPR) at high magnetic fields and frequencies. It uses a superconducting quantum interference device (SQUID) for measuring the magnetic moment as a function of the applied magnetic field and microwave frequency. We used powdered 2,2-diphenyl-1-picrylhydrazyl to demonstrate resolution of g-tensor anisotropy to 1 mT in a magnetic field of 3 T with a sensitivity of 1014 spins per 0.1 mT. We demonstrate multifrequency operation at 95 and 141 GHz. By use of an aligned single crystal of cupric sulfate pentahydrate (chalcanthite) CuSO4∙5H2O, we show that the spectrometer is capable of EPR line shape analysis from 4 to 200 K with a satisfactory fit to a Lorentzian line shape at 100 K. Below 100 K, we observed line-broadening, g shifts, and spectral splittings, all consistent with a known low-dimensional phase transition. Using SQUID magnetometry and a superconducting magnet, we improve by an order of magnitude the sensitivity and magnetic field range of earlier power saturation studies of CuSO4∙5H2O. We were able to saturate up to 70% of the magnetic moment with power transfer saturation studies at 95 GHz, 3.3 T, and 4 K - and obtained the spin-lattice relaxation time, T1=1.8 ms, of CuSO4∙5H2O at 3.3 T and 4 K. We found an inverse linear dependence of T1, in units of seconds (s) at 3.3 T between 4 and 2.3 K, such that T1=0.016∙K∙s∙τ-1-0.0022∙s, where τ is the absolute bath temperature. The quantitative determination of EPR is difficult with standard EPR techniques, especially at high frequencies or fields. Therefore this technique is of considerable value.