We report on a series of composites based on a polymer of intrinsic microporosity matrix (PIM-1) containing a high surface area porous aromatic framework filler (PAF-1). The hydrogen uptake and mechanical properties of the composites are presented along with an assessment of their potential for integration into high-pressure hydrogen storage tanks, either to increase storage capacity or to reduce operating pressure for the same uptake. The composites are more stable and processable than systems such as finely divided physisorbent materials, and they can be made into self-standing films. In addition to retaining the processability of PIM-1, they also possess enhanced surface areas and pore volumes approximately proportional to the amount of incorporated PAF-1. Hydrogen uptake measurements combined with theoretical modelling show that the composites can store up to 6.7 wt% H2 at 77.4 K. Tensile testing and dynamic mechanical thermal analyses indicate decreasing stress and strain to failure with increasing proportion of PAF-1, although the processability and elasticity of the compounds are maintained until the weight percentage of filler reaches 30%. These lightweight composites show promise as effective hydrogen storage materials, especially for applications where pressures up to 7.5 MPa are required. We also provide guidelines for the design of polymer-based porous composites for gas storage or separation.