The use of additive manufacturing technologies for biomedical applications must begin with the knowledge of the material to be used, by envisaging a very specific application rather than a more general aim. In this work, the preliminary study was focused on considering the cartilaginous tissue. This biological tissue exhibits different characteristics, such as thickness and mechanical properties, depending on its specific function in the body. Due to the lack of vascularization, cartilage is a supporting connective tissue with limited capacity for recovery and regeneration. For this reason, any approach, whether to repair/regenerate or as a total replacement, needs to fulfill the adequate mechanical and chemical properties of the surrounding native cartilage to be successful. This work aims to explore the possibility of using new polymers for cartilage total replacement approaches with polymeric materials processed with the specific 3D printing technique of fused filament fabrication (FFF). The materials studied were Nylon® 12 (PA12), already described for this purpose, and LAY-FOMM® 60 (FOMM). FOMM has not been described in the literature for biomedical purposes. Therefore, the chemical, thermal, swelling capacity, and mechanical properties of the filaments were thoroughly characterized to better understand the structure–properties–application relationships of this new polymer. In addition, as the FFF technology is temperature based, the properties were also evaluated in the printed specimens. Due to the envisaged application, the specimens were also characterized in the wet state. When comparing the obtained results with the properties of native cartilage, it was possible to conclude that: (i) PA12 exhibits low swelling capacity, while FOMM, in its dry and wet forms, has a higher swelling capacity, closer to that of native cartilage; (ii) the mechanical properties of the polymeric materials, especially PA12, are higher than those of native cartilage; and (iii) from the mechanical properties evaluated by ultra-micro hardness tests, the values for FOMM indicate that this material could be a good alternative for cartilage replacement in older patients. This preliminary study, essentially devoted to expanding the frontiers of the current state of the art of new polymeric materials, provides valuable indications for future work targeting the envisaged applications.