Solving the phase ambiguity problem is crucial to achieving a wide-range and high-precision measurement for the frequency-domain sampling (FDS)-based surface acoustic wave (SAW) delay-line sensor systems. This study proposes an improved phase estimation algorithm called dual-band phase estimation (DBPE) to solve the problem. By using DBPE, the SAW sensor system can obtain an extensive and alterable measuring range without further requirements for sensor design or transmitted signals. Thus, it can be widely used in various FDS-based SAW delay-line sensor systems. Monte Carlo simulations and temperature measuring experiments, based on a YZ-cut LiNbO3 SAW delay-line sensor and a switched frequency-stepped continuous wave (S-FSCW) reader, are performed to demonstrate the algorithm's validity. The Monte Carlo simulations show that DBPE can effectively solve the phase ambiguity problem and has better performance than frequency estimation in measuring precision at a low signal-to-noise ratio (SNR). The temperature-sensing experiments show that DBPE has a good performance in measuring range and precision, serving as a phase ambiguity solver in the temperature sensor system.