In the present study the interaction of a sine-Gordon kink with a localized inhomogeneity is considered. In the absence of dissipation, the inhomogeneity considered is found to impose a potential energy barrier. The motion of the kink for near-critical values of velocities separating transmission from barrier reflection is studied. Moreover, the existence and stability properties of the kink at the relevant saddle point are examined and its dynamics is found to be accurately captured by effective low-dimensional models. In the case where there is dissipation in the system, below the threshold value of the current, a stable kink is found to exist in the immediate vicinity of the barrier. The effective particle motion of the kink is investigated obtaining very good agreement with the result of the original field model. Both one and two degree-of-freedom settings are examined with the latter being more efficient than the former in capturing the details of the kink motion.