waves emanating out of an LC-circuit

It is absolutely valid to say that in an \(LC\)-circuit the energy is stored as magnetic and electric field energy in the coil and the capacitor, respectively, in an alternating way. On the other hand, this statement would be wrong for the electromagnetic wave emanating from the circuit, because in an electromagnetic plane wave, places with zero magnetic field energy are at the same time places of zero electric field energy. Can you resolve this?