In a vacuum the scalar field 4 and vector field A of electromagnetic radiation satisfy wave equations. Certain mathematically natural measures of energy density and power flux arise for any solutions of any wave equation, and, as components of a conservation law, these measures are utilized like Lyapunov functions in an associated PDE stability theory [Hahn, Stability of Motion, Springer-Verlag, New York, 1967, pp. 216’217], [Walker, Dynamical Systems and Evolution Equations, Plenum, New York, 1990, p. 106], [Zachmanoglov and Thoe, Introduction to Partial Differential Equations with Applications, Dover, New York, 1986, p. 283]. But energy conservation in electrodynamics is conventionally accounted for with the Poynting equation, another mathematical conservation law. The purpose of this paper is to compare the contending measures and conservation laws. A consequence of the new measures is that power flux vanishes if the scalar and vector potentials are constant with respect to time, in contrast to the Poynting system. The new measures also provide an alternative to the classical Larmor formula for radiation from an accelerating charged particle. Concerning antennas, it can be shown that the alternative measure of power radiated from an idealized dipole antenna is about twice that predicted by the Poynting vector. It should be possible to measure carefully antenna power input and perhaps heating to test this prediction. Certain idealized capacitors might also be experimentally approximated to test mathematical predictions of power consumption. The new energy density and power flux can be couched in tensor theory, and this leads to an energy tensor with nonzero trace in the presence of radiation and absence of matter. (The analogous tensor built from the Poynting measure discriminates between those forms of energy, a fact that once led Einstein to propose changing the Einstein field equation.) Thus the range of physical implications of the new conservation law is considerable.