Microresonators with high Q-factor are essential components for optomechanical experiments. Here we report on the development of 'cat-flap' micro-pendulums consisting of sub-millimetre scale micromirrors supported by nanometre-thickness flexures. The micromirror pendulum is designed to achieve the lowest possible flexure stiffness, which enables maximal dilution of mechanical losses through the use of optical springs. An angular spring constant of, corresponding to a fundamental frequency (in the absence of gravity) of 18 Hz has been demonstrated. It is shown that Q-factors up to at an optical spring frequency of 25 kHz could be achieved with these pendulums. By extrapolating the measurement results to a sample with a double thickness mirror pad, we estimate that it may be possible to achieve a Q-factor of at 100 kHz at room temperature.