We consider Extended Theories of Gravity and in particular, models containing scalar-tensor and higher-order curvature terms, as well as models derived from fundamental theories like Non-commutative Spectral Geometry. In the weak-field approximation, we take into account the geodesic and Lense-Thirring processions, deriving constraints on the free parameters by the experimental data on Solar System scales. The main result of this research is that constraints on fundamental theories of gravity can be achieved at local scales and compared with cosmic data.