The influence of a conducting layer on the magnetic flux penetration in a superconducting Nb film is studied by magneto-optical imaging. The metallic layer partially covering the superconductor provides an additional velocity-dependent damping mechanism for the flux motion that helps to protect the superconducting state when thermomagnetic instabilities develop. If the flux advances with a velocity slower than w = 2 / μ 0 σ t , where σ is the cap layer conductivity and t is its thickness, the flux penetration remains unaffected, whereas for incoming flux moving faster than w , the metallic layer becomes an active screening shield. When the metallic layer is replaced by a perfect conductor, it is expected that the flux braking effect will occur for all flux velocities. We investigate this effect by studying Nb samples with a thickness step. Some of the observed features, namely the deflection of the flux trajectories at the border of the thick center, as well as the favored flux penetration at the indentation, are reproduced by time-dependent Ginzburg-Landau simulations.