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The traditional description of the orbital evolution of compact-object binaries, like double white dwarfs (DWDs), assumes that the system is driven only by gravitational wave (GW) radiation. However, the high magnetic fields with intensities of up to gigagauss measured in WDs alert a potential role of the electromagnetic (EM) emission in the evolution of DWDs. We evaluate the orbital dynamics of DWDs under the effects of GW radiation, tidal synchronization, and EM emission by a unipolar inductor generated by the magnetic primary and the relative motion of the non-magnetic secondary. We show that the EM emission can affect the orbital dynamics for magnetic fields larger than megagauss. We applied the model to two known DWDs, SDSS J0651+2844 and ZTF J1539+5027, for which the GW radiation alone does not fully account for the measured orbital decay rate. We obtain upper limits to the primary's magnetic field strength, over which the EM emission causes an orbital decay faster than observed. The contribution of tidal locking and the EM emission is comparable, and together they can contribute up to $20\%$ to the measured orbital decay rate. We show that the gravitational waveform for a DWD modeled as purely driven by GWs and including tidal interactions and EM emission can have large relative dephasing detectable in the mHz regime of frequencies relevant for space-based detectors like LISA. Therefore, including physics besides GW radiation in the waveform templates is essential to calibrate the GW detectors using known sources, e.g., ZTF J1539+5027, and to infer binary parameters.