Narrowband microwave filters have wide ranging applications, including the reduction in phase noise of microwave sources within a given frequency band. The prospect of developing an automated filter that tunes itself to an arbitrary desired frequency at maximum extinction promises many experimental advantages such as an enhanced efficiency in performing fine frequency detuning scans and saving time and effort as compared to manual tuning. We design, construct, and program such an automated system and present its hardware and software for reproducibility. It consists of a cylindrical cavity filter and two motors, which change the cavity length and the coupling strength of the microwave field into the cavity, respectively. By measuring the cavity response, an algorithm implemented in Python optimizes these two parameters to achieve the tuning of the filter cavity to the desired frequency with a precision of around 20 kHz, which is significantly better than the cavity linewidth (similar to 1 MHz). We also demonstrate the suppression of phase noise at the desired frequency by more than 10 dB.