Metamaterials, with their engineered electromagnetic properties not found in nature, hold immense potential for revolutionizing various technological domains. However, their effective design and implementation necessitate accurate characterization and homogenization, particularly for nanostructured metamaterials where challenges abound due to their subwavelength features and complex interactions. This chapter provides a comprehensive overview of electromagnetic characterization and homogenization techniques for nanostructured metamaterials, with a focus on the Kramers-Kronig-based parameter extraction method. We delve into the theoretical foundations of effective medium theory and Kramers-Kronig relations, highlighting their relevance to metamaterial characterization. We explore the Nicolson-Ross-Weir (NRW) method for parameter retrieval and discuss the branching problem associated with refractive index extraction. We then elaborate on how Kramers-Kronig relations can be leveraged to resolve this ambiguity and ensure the physical consistency of the retrieved parameters. The chapter presents case studies involving homogeneous and complex metamaterial structures, demonstrating the effectiveness of the Kramers-Kronig approach in accurately characterizing their electromagnetic behavior. We also discuss advanced topics such as anisotropic materials, nonlocal effects, and nonlinear metamaterials, highlighting future research directions in the field. By bridging the gap between theoretical understanding and practical implementation, this chapter equips readers with the knowledge and tools to effectively characterize and harness the unique properties of nanostructured metamaterials for a wide range of applications.