Polymers of intrinsic microporosity (PIMs) are currently attracting interest due to their unusual combination of high surface areas and capability to be processed into free-standing films. However, there has been little published work with regards to their physical and mechanical properties. In this paper, detailed characterisation of PIM-1 was performed by considering its chemical, gas adsorption and mechanical properties. The polymer was cast into films, and characterised in terms of their hydrogen adsorption at −196 °C up to much higher pressures (17 MPa) than previously reported (2 MPa), demonstrating the maximum excess adsorbed capacity of the material and its uptake behaviour in higher pressure regimes. The measured tensile strength of the polymer film was 31 MPa with a Young’s modulus of 1.26 GPa, whereas the average storage modulus exceeded 960 MPa. The failure strain of the material was 4.4%. It was found that the film is thermally stable at low temperatures, down to −150 °C, and decomposition of the material occurs at 350 °C. These results suggest that PIM-1 has sufficient elasticity to withstand the elastic deformations occurring within state-of-the-art high-pressure hydrogen storage tanks and sufficient thermal stability to be applied at the range of temperatures necessary for gas storage applications.