One method as described herein relates to making a high molecular weight, monoesterified polyimide polymer using a small amount of bulky diamine. These high molecular weight, monoesterified polyimide polymers are useful in forming crosslinked polymer membranes with high permeance that are useful for the separation of fluid mixtures. Another method as described herein relates to making the crosslinked membranes from the high molecular weight, monoesterified polyimide polymer containing a small amount of bulky diamine. The small amount of bulky diamine allows for formation of both the high molecular weight polyimide polymer and for covalent ester crosslinks via reaction of the carboxylic acid groups with a diol crosslinking agent. This small amount of bulky diamines reduces chain mobility or segmental motion during crosslinking and reduces large loss of permeance. As such, this method provides a crosslinked membrane with good permeance and selectivity.