Intrinsic permeability describes the ability of a porous medium to be penetrated by a fluid. Considering porous scaffolds for tissue engineering (TE) applications, this macroscopic variable can strongly influence the transport of oxygen and nutrients, the cell seeding process, and the transmission of fluid forces to the cells, playing a crucial role in determining scaffold efficacy. Thus, accurately measuring the permeability of porous scaffolds could represent an essential step in their optimization process. In literature, several methods have been proposed to characterize scaffold permeability. Most of the currently adopted approaches to assess permeability limit their applicability to specific scaffold structures, hampering protocols standardization, and ultimately leading to incomparable results among different laboratories. The content of novelty of this study is in the proposal of an adaptable test bench and in defining a specific testing protocol, compliant with the ASTM International F2952-22 guidelines, for reliable and repeatable measurements of the intrinsic permeability of TE porous scaffolds. The developed permeability test bench (PTB) exploits the pump-based method, and it is composed of a modular permeability chamber integrated within a closed-loop hydraulic circuit, which includes a peristaltic pump and pressure sensors, recirculating demineralized water. A specific testing protocol was defined for characterizing the pressure drop associated with the scaffold under test, while minimizing the effects of uncertainty sources. To assess the operational capabilities and performance of the proposed test bench, permeability measurements were conducted on PLA scaffolds with regular (PS) and random (RS) micro-architecture and on commercial bovine bone matrix-derived scaffolds (CS) for bone TE. To validate the proposed approach, the scaffolds were as well characterized using an alternative test bench (ATB) based on acoustic measurements, implementing a blind randomized testing procedure. The consistency of the permeability values measured using both the test benches demonstrated the reliability of the proposed approach. A further validation of the PTB’s measurement reliability was provided by the agreement between the measured permeability values of the PS scaffolds and the theory-based predicted permeability value. Once validated the proposed PTB, the performed measurements allowed the investigation of the scaffolds’ transport properties. Samples with the same structure (guaranteed by the fused-deposition modeling technique) were characterized by similar permeability values, and CS and RS scaffolds showed permeability values in agreement with the values reported in the literature for bovine trabecular bone. In conclusion, the developed PTB and the proposed testing protocol allow the characterization of the intrinsic permeability of porous scaffolds of different types and dimensions under controlled flow regimes, representing a powerful tool in view of providing a reliable and repeatable framework for characterizing and optimizing scaffolds for TE applications.