A computationally inexpensive magnetic equivalent circuit (MEC) improves axisymmetric electromagnet design and modeling tools by accurately capturing fringing and leakage effects. Lumped parameter MEC models are typically less accurate for modeling electromagnetic devices than distributed parameter finite-element models (FEMs). However, MEC models require significantly less computational time to solve than FEMs and therefore lend themselves to applications where solution time is critical, such as in optimization routines, dynamic simulation, or preliminary design. This paper describes how fringing permeances in axisymmetric electromagnetic devices can be derived and then included in a MEC model. Including fringing field effects significantly decreases error in the MEC model, creating a more accurate, or high fidelity, magnetic equivalent circuit (HFMEC). Eighty-nine electromagnets with unique geometries, coil currents, and materials were modeled with MEC, HFMEC, and FEM methods. The axisymmetric HFMEC developed in this work had 67% less average force error and 88% less average flux error compared to traditional MEC results while still being computationally inexpensive to solve.