  Inclusive production processes will be important for the first observations
of $XYZ$ states at new generation electron-hadron colliders, as they generally
benefit from larger cross sections than their exclusive counterparts. We make
predictions of semi-inclusive photoproduction of the $\chi_{c1}(1P)$ and
$X(3872)$, whose peripheral production is assumed to be dominated by vector
exchanges. We validate the applicability of Vector Meson Dominance in the
axial-vector charmonium sector and calculate production rates at center-of-mass
energies relevant for future experimental facilities. We find the
semi-inclusive cross sections near threshold to be enhanced by a factor of
$\sim 2-3$ compared to the exclusive reaction and well suited for a first
observation in photoproduction.
