With the growing number of zeolites and metal-organic frameworks (MOFs) available, computational methods are needed to screen databases of structures to identify those most suitable for applications of interest. We have developed novel methods based on mathematical optimization to predict the shape selectivity of zeolites and MOFs in three dimensions by considering the energy costs of transport through possible pathways. Our approach is applied to databases of over 1800 microporous materials including zeolites, MOFs, zeolitic imidazolate frameworks, and hypothetical MOFs. New materials are identified for applications in gas separations (CO2/N2, CO2/CH4, and CO2/H2), air separation (O2/N2), and chemicals (propane/propylene, ethane/ethylene, styrene/ethylbenzene, and xylenes).