Wave-based structural identification for real honeycomb sandwich structures has become an important research focus. However, most existing wave-based identification methods suffers from experimental uncertainties and a limited frequency range of applicability. To this end, we present a new wave-based structural identification framework, which includes two promising material identification methods – linear and nonlinear – suitable for honeycomb sandwich structures. The advantages of the identification process are reflected on two aspects: Firstly, the Algebraic Wavenumber Identification (AWI) technique reliably extracts complex wavenumbers over a wide frequency range under stochastic conditions, serving as input for the identification process. Secondly, a novel frequency-dependent, stepwise estimation strategy is proposed for honeycomb sandwich structures, greatly enhancing the precision of material parameter determination. Noteworthy, the proposed structural identifications enable the recovery of both equivalent dynamic and static mechanical properties. The experimental applications on a real beam, plate, and shell are presented. Key results show that (1) The proposed stepwise strategy reduces the relative error of wavenumbers of the tested beam to below 3.5%, improving parameter accuracy and ensuring estimation success; (2) For the tested plate, the estimated Young's modulus of skins, shear modulus of the core, and dynamic Hooke's matrix demonstrate satisfied precision; (3) It is the first to extract mechanical parameters of real curved structures using wave-based propagation parameters.