Abstract We briefly review the phenomenology of flux trapping in superconductors and its relevance to Fundamental Physics experiments such as STEP. We develop mathematical expressions which enable force and force gradients acting on two imperfect superconducting planes to be calculated from magnetic field measurements across their surfaces. We use the results of this analysis to estimate the magnitude of differential acceleration noise coupling to a STEP test mass pair due to spacecraft displacement and find the following constraint δ c≤10 −3 x·· 10 −15ms −2/ Hz 1 2 m 200g 1 mG B r 2 1 cm a 2Hz − 1 2 where δ is the spacecraft displacement amplitude spectral density, c is the spacing between superconducting surfaces of net surface area a 2. The desired experimental noise sensitivity is ẍ, the test mass value is m and B r is the value of the residual magnetic field in the STEP dewar. We further use our models to analyse the possibility of inhibiting the rotation of the test masses about the bearing axis by creating a regular array of trapped-flux lines on the test mass surfaces. The results of our preliminary calculations suggest that this idea may not be viable.