This paper proposes a technique for rapid high fidelity finite element based synchronous machine models for use in system simulators. The computational efficient finite element procedure, CE-FEA, is used to construct harmonic flux linkage arrays for a range of current inputs. In the system simulator, a map is constructed relating rotor position as an input to relate instantaneous flux linkage and d and q axis currents. Using rotor position and flux linkages as inputs from the system simulator and interpolating the flux linkage map, the phase currents of the synchronous machine are determined. In the system simulation, the phase currents are modeled as dependent current sources. This technique allows for the modeling of space and time harmonics, saturation, and cogging torque within the system simulator without directly coupling the finite element solver. Three examples of system simulation results are shown for an interior permanent magnet synchronous machine.