  In this work, we compute some phenomenological bounds for the electromagnetic
and massive gravitational high-derivative extensions supposing that it is
possible to have an astrophysical process that generates simultaneously
gravitational and electromagnetic waves. We present Lorentz invariance
violating (LIV) higher-order derivative models, following the Myers-Pospelov
approach, to electrodynamics and massive gravitational waves. We compute the
corrected equation of motion of these models, their dispersion relations and
the velocities. The LIV parameters for the gravitational and electromagnetic
sectors, $\xi_{g}$ and $\xi_{\gamma}$, respectively, were also obtained for
three different approaches: luminal photons, time delay of flight and the
difference of graviton and photon velocities. These LIV parameters depend on
the mass scales where the LIV-terms become relevant, $M$ for the
electromagnetic sector and $M_{1}$ for the gravitational one. We obtain, using
the 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 phenomenological
point of view if $M\gg M_{1}$. Finally the relation between the variation of
the velocities of the photon and the graviton in relation to the speed of light
was calculated and resulted in $\Delta v_{g}/\Delta
v_{\gamma}\lesssim1.82\times 10^{-3}$.
