The careful filtering of microwave electromagnetic radiation is critical for controlling the electromagnetic environment for experiments in solid-state quantum information processing and quantum metrology at millikelvin temperatures. We describe the design and fabrication of a coaxial filter assembly and demonstrate that its performance is in excellent agreement with theoretical modelling. We further perform an indicative test of the operation of the filters by making current-voltage measurements of small, underdamped Josephson junctions at 15 mK.