The increase in rainfall intensity caused by climate change, combined with high levels of urban soil sealing and the limited capacity of drainage systems, is significantly increasing flooding risk. Integrated stormwater management is a key factor in dealing with the consequences of climate change by mitigating flood risk based on nature-based solutions. An experimental site was designed to assess the hydrological response of vegetated swales depending on different catchment surfaces, and to evaluate the impact of spatial variability of the hydraulic conductivity (K). A hydrological model was developed on EPA SWMM and calibrated based on measured data in two experimental swales with different active surfaces (N6—50 m2 and N11—100 m2). The model validation was assessed with NSE scores higher than 0.7. The simulations considered various factors, such as the water level in the swales, the actual rainfall, the evapotranspiration, the swale geometry, the catchment area (Sa), and the hydraulic conductivities of the natural silty soil, to assess, for the heaviest rainfall event, the best swale morphological characteristics. The study examined the combined impact of K (8) and Sa (6) on swale storage capacity, designed with a 250 mm depth. The simulations showed that the 250 mm overflow limit was exceeded for N10 (90 m2) when K ≤ 2 × 10−6 m/s, and for N11 (100 m2) when K ≤ 4 × 10−6 m/s. These results provide valuable information on the optimal storage capacity based on the swales’ geometrical and physical properties.