This paper establishes the meromorphic continuation of the semiclassical resolvent associated to pseudodifferential operators with normally hyperbolic trapped sets. By employing escape function constructions and anisotropic Sobolev spaces (Dyatlov-Zworski framework), we define H_{G}^{s} := e^{-G^{w}/h}H^{s} to recover a Fredholm setting. The poles of the continued resolvent are shown to characterize the quantum resonances of the system.