A novel low-cost microwave sensor system is proposed for accurate sensing of the real relative permittivity of materials under test (MUT). The proposed solution eliminates the need for using advanced measurement devices such as the vector network analyzer (VNA) for sensor characterization. The proposed sensor system is built on a software-defined radio platform. A suitable two-stage frequency estimation approach was developed for estimating the frequency shift of the resonator sensor associated with the real relative permittivity of the MUT. First, the neighborhood of the resonance frequency is obtained utilizing a low-resolution coarse search, followed by a fine search method to accurately estimate the resonance frequency. For the fine search, we modified the AM frequency estimation algorithm and the Golden Section search algorithm to suite the proposed sensor system. The performance of the proposed sensor system is validated through simulations and experiments. To demonstrate the feasibility of the concept, experiments were conducted by implementing the solution on a Universal Software Radio Peripheral transceiver using a resonator sensor for detecting the binary mixture of water and methanol. The results show that the proposed sensor system achieves measurement accuracy comparable to advanced equipment such as the VNA. Thus, the proposed sensor system could be a low-cost alternative for sensor characterization purposes with accuracy comparable to standard equipment.