This paper presents a photonics-based instantaneous microwave frequency measurement system. The system operates based on the frequency-to-power mapping technique. The trade-off between frequency measurement range and resolution, which is present in the reported frequency-to-power-mapping based frequency measurement systems, is addressed by designing the system to produce two amplitude comparison functions (ACFs). Using two ACFs enables an RF signal frequency in a specified range to be determined while having an improved resolution and smaller errors compared to using only one ACF for frequency measurement. The proposed frequency measurement system is designed to have a simple structure and robust performance suitable for use in real world applications. The effect of the higher order sidebands and harmonics on the system performance are investigated. Proof-of-concept experiments are carried out with results showing frequency measurement errors can be reduced by using the proposed system that generates two ACFs for frequency measurement.