  A challenge to standard leptonic SSC models are so-called orphan TeV flares,
i.e. enhanced very high energy (VHE) gamma-ray emission without any
contemporaneous X-ray flaring activity, that have recently been observed in
TeV-blazars (e.g., 1ES 1959+650). In order to explain the orphan TeV flare of
1ES 1959+650 observed in June 2002, the co-called hadronic synchrotron mirror
model has been developed. Here, relativistic protons are proposed to exist in
the jet, and interact with reflected electron-synchrotron radiation of the
precursor SSC flare. If the reflector is located in the cloud region, time
shifts of several days are possible between the precursor and the orphan flare.
The external photons, blueshifted in the comoving jet frame, are able to excite
the \Delta(1232)-resonance when interacting with protons of Lorentz factors
\gamma'_p~10^3-10^4. The decay products of this resonance include charged pions
which, upon decay, give rise to neutrino production during the orphan flare. In
this paper we calculate the expected neutrino emission for the June 4, 2002,
orphan TeV flare of 1ES 1959+650. We compare our results with the recent
observations of AMANDA-II of a neutrino event in spatial and temporal
coincidence with the orphan flare of this blazar. We find that the expected
neutrino signal from the hadronic synchrotron mirror model is insufficient to
explain the observed neutrino event from the direction of 1ES 1959+650.
