  We consider a classical Heisenberg model on the kagom\'{e} and the square
kagom\'{e} lattice, where at zero magnetic field non-coplanar cuboctahedral
ground states with twelve sublattices exist if suitable exchange couplings are
introduced between the other neighbors. Such 'cuboc ground states' are
remarkable because they allow for chiral ordering. For these models, we discuss
the magnetization process in an applied magnetic field $H$ by both numerical
and analytical methods. We find some universal properties that are present in
all models. The magnetization curve $M(H)$ usually contains only non-linear
components and there is at least one magnetic field driven phase transition.
Details of the $M(H)$ curve such as the number and characteristics (continuous
or discontinuous) of the phase transitions depend on the lattice and the
details of the exchange between the further neighbors. Typical features of
these magnetization processes can already be derived for a paradigmatic 12 spin
model that we define in this work.
