  We construct the $\mathcal{N}=2$ supersymmetric extensions of different
models containing a Chern-Simons term and study their BPS structure. We find
that the coupling of the Chern-Simons term to the general gauged nonlinear
$\sigma$-model allows for general potentials depending on the K\"{a}hler metric
and preserving two supersymmetries. We construct from supersymmetry the
potentials that allow for BPS structures in different $\mathbb{C}P^{N}$ models
coupled to Chern-Simons and Maxwell terms. We also couple the Chern-Simons term
to a higher-derivative field theory (the baby Skyrme model) and study its SUSY
extension and BPS structure.
