Recently, a commercial treatment planning system (TPS) has implemented aperture collimators for PBS dose calculations which can serve to reduce lateral penumbra. This study characterized the variation in magnitude of lateral penumbra for collimated and un-collimated PBS fields versus the parameters of air gap, depth, and range shifter thickness. Comparisons were performed in a homogenous geometry between measured data and calculations made by a commercial TPS. Beam-specific target volumes were generated for collimated and un-collimated PBS fields and optimized for various range shifter thicknesses and air gaps. Lateral penumbra (80%-20% distance) was measured across each target volume to characterize penumbra variation with depth and air gap. An analytic equation was introduced to predict the reduction in lateral penumbra between un-collimated and collimated PBS treatments. Calculated penumbra values increased with depth across all combinations of range shifters for a constant air gap. At 2 cm depth, the reductions in penumbra due to the aperture were 2.7 mm, 3.7 mm and 4.2 mm when using range shifter thicknesses of 0 cm, 4.0 cm and 7.5 cm, respectively. At a depth of approximately 20 cm and air gap of 5 cm, differences between penumbras of collimated and un-collimated beams were less than 1 mm. Penumbra reductions for the collimated beams were largest at small air gaps. All TPS-calculated penumbra values derived in this study were within 1 mm of film measurement values. Finally, the analytic equation was tested using a clinical CT scan, and we found good dosimetric agreement between the model predictions and the result calculated by the TPS. In conclusion, application of collimators to PBS fields can sharpen penumbra by several mm and are most beneficial for shallow targets. Furthermore, measurements indicate that the dose calculation accuracy in the penumbra region of PBS-collimated fields is adequate for clinical use.