In this talk we show tailored model order reduction (MOR) techniques for boundary optimal control problems governed by a parametric partial differential equation (PDE) in which at least one of the parameters changes how the boundary control acts on the system. This model can be used in many applied fields, such as geophysics and energy engineering, to obtain fast and reliable solutions. The variation of the geometry of the boundary control leads to a complex behaviour of the state and the adjoint variables, such as transport-like phenomena in the state variable. Moreover, the affine structure of the problem is lost. We propose and compare different reduced approacches, inspired by the ones used with wave-like phenomena, to obtain good accuracy and efficiency performances even in complex geometries, which classical reduction techniques are not able to provide.