Pinching antenna systems (PASS) have emerged as a promising architecture for high-frequency wireless communications. In this letter, we investigate user localization in PASS by jointly exploiting the received signal amplitude and phase information. A complex baseband signal model is formulated to capture free-space path loss, waveguide attenuation, and distance-dependent phase rotation between the user and each pinching antenna. Based on this model, we derive the Fisher information matrix and closed-form Cramer-Rao lower bound and position error bound. The derived analysis reveals that the phase-induced Fisher information decays with the fourth power of the user-antenna distance, whereas the amplitude-induced information decays with the sixth power, explaining the fundamental advantage of phase-aware localization in typical PASS deployments. A maximum likelihood estimator is then developed and implemented through a two-stage procedure combining coarse grid search and Levenberg-Marquardt refinement. Numerical results show that the proposed estimator achieves low positioning error and generally outperforms the considered benchmarks under different noise powers, numbers of pinching antennas, and user locations. In the considered scenario, the proposed method achieves sub-meter-level accuracy over the evaluated service area and yields substantially lower positioning error than the amplitude-only benchmark.

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