Abstract: We describe methods for polynomial reconstruction of the magnetic field close to a cluster of 4 spacecraft, and apply that to reconstruction of the magnetic field observed during magnetic reconnection events observed by the Magnetospheric Multiscale (MMS) spacecraft and to data from virtual MMS spacecraft flying through a simulation of magnetopause reconnection . Four different models are described, which vary in complexity between a 12 parameter Linear model, that has only linear variation with respect to the spatial coordinates, and a 27 parameter Quadratic model, that has the full quadratic expansion except that the second derivative with respect to the Minimum Directional Derivative (MDD) minimum gradient coordinate m has been neglected. Two other intermediate models neglect additional terms. The 3D Reduced quadratic model neglects all but linear variation with respect to m and neglects additional terms in order to keep partial-Bn / partial-n small, where n is the coordinate varying across the current sheet. We show that the 3D Reduced quadratic model and the other intermediate model have very small errors in the magnetic field (< 0.1 nT) at a distance on the order of the spacecraft separation, Lsc, equal to 20.5 km for this event. The magnetic structures found for an MMS event observed on 10 Aug 2017 using this model are very time-dependent, with a stretched field leading to plasmoid formation at one point in time. The reconstructions of the simulated data are very good on the magnetosheath side of the current sheet, where the magnetic field is more distorted, but much worse on the magnetosphere side, where the parameters of the models are determined from small variations in the magnetic field.