The polymer of intrinsic microporosity PIM‐EA‐TB provides a molecularly rigid micropore structure containing tertiary amine sites and is shown here to interact with hydrogen bonding guest molecules such as caffeic acid. Voltammetric data with a PIM‐EA‐TB film on glassy carbon electrodes show that in both acidic solution (pH 2; PIM‐EA‐TB is protonated) and in neutral solution (pH 6; PIM‐EA‐TB is not protonated) caffeic acid is slowly accumulated into the microporous host. Binding constants are estimated and suggested to be linked to hydrogen bonding causing accumulation of caffeic acid. When employing PIM‐EA‐TB as an asymmetric membrane coated onto a 5 mm thick Teflon support film with 10 mm diameter microholes (using either a single microhole or a 10 × 10 array of microholes), binding of caffeic acid is shown to cause a modulation of the ionic current without affecting the pH‐dependent ionic diode behaviour. Two complementary types of effects of caffeic acid guests are discussed based on blocking anion diffusion pathways and based on removal of positive charges. The caffeic acid transport mechanism/efficiency is investigated in view of selective molecular pumping.