Some organic cage molecules have structures with protected, internal pore volume that cannot be in-filled, irrespective of the solid-state packing mode: that is, they are intrinsically porous. Amorphous packings can give higher pore volumes than crystalline packings for these materials, but the precise nature of this additional porosity is hard to understand for disordered solids that cannot be characterized by X-ray diffraction. We describe here a computational methodology for generating structural models of amorphous porous organic cages that are consistent with experimental data. Molecular dynamics simulations rationalize the observed gas selectivity in these amorphous solids and lead to insights regarding self-diffusivities, gas diffusion trajectories, and gas hopping mechanisms. These methods might be suitable for the de novo design of new amorphous porous solids for specific applications, where "rigid host" approximations are not applicable.