  The application of Very Long Baseline Interferometry (VLBI) to the Search for
Extraterrestrial Intelligence (SETI) has been limited to date, despite the
technique offering many advantages over traditional single-dish SETI
observations. In order to further develop interferometry for SETI, we used the
European VLBI Network (EVN) at $21$~cm to observe potential secondary phase
calibrators in the Kepler field. Unfortunately, no secondary calibrators were
detected. However, a VLBA primary calibrator in the field, J1926+4441, offset
only $\sim1.88'$ from a nearby exoplanet Kepler-111~b, was correlated with high
temporal $\left(0.25 \ \rm{s}\right)$ and spectral $\left(16384 \times 488\
\rm{Hz \ channels}\right)$ resolution. During the analysis of the
high-resolution data, we identified a spectral feature that was present in both
the auto and cross-correlation data with a central frequency of
$1420.424\pm0.0002$ MHz and a width of 0.25 MHz. We demonstrate that the
feature in the cross-correlations is an artefact in the data, associated with a
significant increase in each telescope's noise figure due to the presence of
\ion{H}{i} in the beam. This would typically go unnoticed in data correlated
with standard spectral resolution. We flag (excluded from the subsequent
analysis) these channels and phase rotate the data to the location of
Kepler-111~b aided by the GAIA catalogue and search for signals with
$\rm{SNR}>7$. At the time of our observations, we detect no transmitters with
an Equivalent Isotropically Radiated Power (EIRP) > $\sim4\times10^{15}$ W.
