A method is described to model the magnetic field in the vicinity of three‐dimensional constellations of satellites (at least four) using field and plasma current measurements. This quadratic model matches the measured values of the magnetic field and its curl (current) at each spacecraft, with ∇ • B zero everywhere, and thus extends the linear curlometer method to second order. Near the spacecraft, it predicts the topology of magnetic structures, such as reconnecting regions or flux ropes, and allows a tracking of the motion of these structures relative to the spacecraft constellation. Comparisons to particle‐in‐cell simulations estimate the model accuracy. Reconstruction of two electron diffusion regions definitively confirms the expected field line structure. The model can be applied to other small‐scale phenomena (e.g., bow shocks) and can also be modified to reconstruct the electric field, allowing tracing of particle trajectories. Key Points Three‐dimensional model of magnetic field is constructed using magnetic field and current data The constructions are able to visualize the local magnetic topology around spacecraft Motion of magnetic structures can be derived