The magnetic flux generated by the screening currents of a superconducting Nb film in the Meissner state is measured with a coaxial gradiometer in a weak magnetic field B. A peculiar position dependence is found when the sample surface is only slightly tilted away from the parallel field orientation and shifted with respect to the center axis of the gradiometer. This is due to the inhomogeneous magnetization with a strong out-of-plane contribution measured by the two pick-up coils as confirmed by numerical finite-element calculations. The unusual position dependence has important consequences for interpreting the diamagnetic screening of superconducting films measured by a coaxial gradiometer near the parallel-field orientation. © 2004 American Institute of Physics.