Weber–Maxwell electrodynamics combines classical Weber electrodynamics and Maxwell’s equations, including all four field equations and the Lorentz force, into a single de facto equivalent 3-D wave equation. From classical Weber electrodynamics, Weber–Maxwell electrodynamics inherits properties in which the concept of the magnetic field is unnecessary, and Newton’s third law is satisfied under all circumstances. From Maxwell’s electrodynamics, Weber–Maxwell electrodynamics inherits the ability to be compatible with electromagnetic waves. This article shows that in Weber–Maxwell electrodynamics, all conservation laws are satisfied, and that electromagnetic waves in an isolated system do not possess energy and momentum, but only mediate them between particles of matter. Furthermore, the article shows that the modern formulation of Weber electrodynamics is clearly superior to standard electrodynamics in electrical engineering, because it not only eliminates internal contradictions, but also represents considerable simplification and compression.