Imine cage molecules can be reduced to amines to improve their chemical stability, but this introduces molecular flexibility. Hence, amine cages tend not to exhibit permanent solid-state porosity. We report a synthetic strategy to achieve shape persistence in amine cages by tying the cage vertices with carbonyls such as formaldehyde. Shape persistence is predicted by conformer stability calculations, providing a design basis for the strategy. The tied cages show enhanced porosity and unprecedented chemical stability toward acidic and basic conditions (pH 1.7-12.3), where many other porous crystalline solids would fail.