  Jets of Active Galactic Nuclei (AGN) are established emitters of very high
energy (VHE; >100 GeV) gamma-rays. VHE radiation is also expected to be emitted
from the vicinity of super-massive black holes (SMBH), irrespective of their
activity state. Accreting SMBH rotate and generate a dipolar magnetic field. In
the magnetosphere of the spinning black hole, acceleration of particles can
take place in the field gaps. VHE emission from these particles is feasible via
leptonic or hadronic processes. Therefore quiescent systems, where the lack of
a strong photon field allows the VHE emission to escape, are candidates for
emission. The H.E.S.S. experiment has observed the passive SMBH in the nearby
galaxy NGC 1399. No VHE gamma-ray signal is observed from the galactic nucleus.
Constraints set by the NGC 1399 observations are discussed in the context of
different mechanisms for the production of VHE gamma-ray emission.
