An study of the one-dimensional isentropic compression experiment (ICE), performed with High Explosive Pulsed Power (HEPP), has demonstrated that accurate, high stress, isentropic Equations of State (EOS) data may be obtained with this technique. The physics and accuracy of electromagnetic loading in the ICE technique is presented. It is shown that the HEPP-ICE load configuration is capable of producing magnetic stresses that are uniform to 1 part in 1000 over the central 87% of the sample faces, and that HEPP-ICE provides exact matching of the stresses between opposing samples. This magnetic uniformity, the exact matching, and the large sample samples possible with HEPP-ICE, are necessary for the highest accuracy isentropic EOS data. Isentropic EOS data have been obtained with a prototype HEPP-ICE system, and the results for tungsten and copper demonstrate the inaccuracy of the technique, which may be as low as 0.2% in stress. It is shown that a large-scale HEPP-ICE system is capable of producing shock-free loading up to 2.2 TPa in 10-mm thick tungsten samples.