Metamaterials are attracting much attention due to their remarkable mechanical properties. They can be tailored to fulfill a specific functionality. However, they usually exhibit size-effects phenomena, indicating that their mechanical behaviors vary when their size changes. To model them as a homogeneous medium, enriched continua theories that capture size-effects are the preferred choice. The relaxed micromorphic model is a generalized continuum that differs from the classical micromorphic theory by using the $\Curl$ of a micro-distortion field instead of the full gradient, however, leading to many advantages such as the notably reduced number of parameters and well-posedness for the symmetric force stress case. The most important advantage is the unique behavior as a macroscopic-microscopic two-scale linear elasticity model, which other generalized continua do not offer. In this work, we use the relaxed micromorphic continuum to model metamaterials. First,  conforming $H^1(\B) \times H(\Curl,\B)$ finite elements are presented and tested in several numerical examples. We systematically investigate the boundary conditions of the micro-distortion field, proving the necessity of the consistent coupling boundary condition.  We identify the microscopic elasticity tensor employing the stiffest response concept under affine and non-affine boundary conditions. Finally, we develop an optimization procedure to define all the unknown parameters through direct energy fitting.