  The blazar Mrk 421 shows frequent, short flares in the TeV energy regime. Due
to the fast nature of such episodes, we often fail to obtain sufficient
simultaneous information about flux variations in several energy bands. To
overcome this lack of multi-wavelength (MWL) coverage, especially for the pre-
and post-flare periods, we have set up a monitoring program with the FACT
telescope (TeV energies) and the Neil Gehrels Swift Observatory (X-rays). On
2019 June 9, Mrk 421 showed a TeV outburst reaching a flux level of more than
two times the flux of the Crab Nebula at TeV energies. We acquired simultaneous
data in the X-rays with additional observations by XMM-Newton and INTEGRAL. For
the first time, we can study a TeV blazar in outburst taking advantage of
highly sensitive X-ray data from XMM-Newton and INTEGRAL combined. Our dataset
is complemented by pointed radio observations by Effelsberg at GHz frequencies.
We present our first results, including the {\gamma}-ray and X-ray light
curves, a timing analysis of the X-ray data obtained with XMM-Newton , as well
as the radio spectra before, during and after the flare.
