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In this work, we compute some phenomenological bounds for the electromagneticand massive gravitational high-derivative extensions supposing that it ispossible to have an astrophysical process that generates simultaneouslygravitational and electromagnetic waves. We present Lorentz invarianceviolating (LIV) higher-order derivative models, following the Myers-Pospelovapproach, to electrodynamics and massive gravitational waves. We compute thecorrected equation of motion of these models, their dispersion relations andthe velocities. The LIV parameters for the gravitational and electromagneticsectors, $\xi_{g}$ and $\xi_{\gamma}$, respectively, were also obtained forthree different approaches: luminal photons, time delay of flight and thedifference of graviton and photon velocities. These LIV parameters depend onthe mass scales where the LIV-terms become relevant, $M$ for theelectromagnetic sector and $M_{1}$ for the gravitational one. We obtain, usingthe values for $M$ and $M_{1}$ found in the literature, that$\xi_{g}\sim10^{-2}$, which is expected to be phenomenologically relevant and$\xi_{\gamma}\sim10^{3}$, which cannot be suitable for an effective LIV theory.However, we show that $\xi_{\gamma}$ can be interesting in a phenomenologicalpoint of view if $M\gg M_{1}$. Finally the relation between the variation ofthe velocities of the photon and the graviton in relation to the speed of lightwas calculated and resulted in $\Delta v_{g}/\Deltav_{\gamma}\lesssim1.82\times 10^{-3}$.

Lorentz invariance violation and simultaneous emission of electromagnetic and gravitational waves