Abstract : We present a new family of high-resolution, non-oscillatory semi-discrete central schemes for the approximate solution of the ideal Magnetohydrodynamics (MHD) equations. This is the second part of our work, where we are passing from the fully-discrete, staggered schemes to a semi-discrete formulation. This semi-discrete formulation retains the simplicity of fully-discrete central schemes while enhancing efficiency and adding versatility. The semi-discrete algorithm offers a wider range of options to implement its two key steps: non-oscillatory reconstruction and evolution. Along with the description of the numerical methods employed, we present several prototype MHD problems.