  We conducted an observational campaign towards one of the most massive and
luminous colliding wind binaries in the Galaxy, HD~93129A, close to its
periastron passage in 2018. During this time the source was predicted to be in
its maximum of high-energy emission. Here we present our data analysis from the
X-ray satellites \textit{Chandra} and \textit{NuSTAR} and the $\gamma$-ray
satellite \textit{AGILE}. High-energy emission coincident with HD~93129A was
detected in the X-ray band up to $\sim$18~keV, whereas in the $\gamma$-ray band
only upper limits were obtained. We interpret the derived fluxes using a
non-thermal radiative model for the wind-collision region. We establish a
conservative upper limit for the fraction of the wind kinetic power that is
converted into relativistic electron acceleration, $f_\mathrm{NT,e} < 0.02$. In
addition, we set a lower limit for the magnetic field in the wind-collision
region as $B_\mathrm{WCR} > 0.3$~G. We also argue a putative interpretation of
the emission from which we estimate $f_\mathrm{NT,e} \approx 0.006$ and
$B_\mathrm{WCR} \approx 0.5$~G. We conclude that multi-wavelength, dedicated
observing campaigns during carefully selected epochs are a powerful tool for
characterising the relativistic particle content and magnetic field intensity
in colliding wind binaries.
