Superglassy polymers have emerged as potential membrane materials for several gas separation applications, including acid gas removal from natural gas. Despite the superior performance shown at laboratory scale, their use at industrial scale is hampered by their large drop in gas permeability over time due to physical aging. Several strategies are proposed in the literature to prevent loss of performance, the incorporation of fillers being a successful approach. In this work, we provide a comprehensive economic study on the application of superglassy membranes in a hybrid membrane/amine process for natural gas sweetening. The hybrid process is compared with the more traditional stand-alone amine-absorption technique for a range of membrane gas separation properties (CO2 permeance and CO2/CH4 selectivity), and recommendations for long-term membrane performance are made. These recommendations can drive future research on producing mixed matrix membranes (MMMs) of superglassy polymers with anti-aging properties (i.e., target permeance and selectivity is maintained over time), as thin film nanocomposite membranes (TFNs). For the selected natural gas composition of 28% of acid gas content (8% CO2 and 20% H2S), we have found that a CO2 permeance of 200 GPU and a CO2/CH4 selectivity of 16 is an optimal target.