Highly detailed models of power converters can be slow to simulate due to the wide disparity in transient time scales. This is further pronounced in the presence of nonlinear components, e.g., saturated inductors. Variable-resolution simulation provides an alternative method by providing an appropriate amount of detail based on the time scale and phenomenon being considered. First, a high-fidelity detailed full-order model of the converter is built that accounts for the system parasitics and higher order effects, component nonlinearity, etc. Efficient order-reduction techniques are then used to extract several lower order models for the desired resolution of the simulation. The state continuity across different resolutions and switching events is ensured using appropriate similarity transforms. The proposed variable-resolution simulation framework is demonstrated on a boost converter with a saturated inductor. Significant improvement in simulation speed (orders of magnitude) is reported.