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The BL Lac type object Mrk 501 was observed at very high energies (E > 100GeV) in 2014 with the upgraded H.E.S.S. (High Energy Stereoscopic System) phase2 array. The data collected with the central 28m telescope allow for a broaderenergy range extending to lower energies when compared to the one obtained withthe four small telescopes alone. A strong flaring event with a flux levelcomparable to the 1997 historical maximum has been detected as a consequence oftarget of opportunity observations triggered by alerts from the FACTcollaboration. The First G-APD Cherenkov Telescope (FACT) is continuouslymonitoring bright blazars at TeV energies providing important pre- andpost-flare information. For the first time, the data and lightcurves fromH.E.S.S. and FACT are compared. These contemporaneous observations allow for abetter characterization of the source emission. In a multiwavelength context,more precise correlation studies between VHE and lower energies are possiblethanks to the dense sampling of the FACT observations. The hard intrinsicspectrum detected by H.E.S.S. during the flare allows the derivation of strongconstraints on the scale of Lorentz invariance violation via the non-detectionof EBL opacity modifications and from time-of-flight studies.

The Exceptional Flare of Mrk 501 in 2014: Combined Observations with H.E.S.S. and FACT