  This paper directly builds upon previous work where we introduced new reduced
basis a posteriori error bounds for parametrized saddle point problems based on
Brezzi's theory. We here sharpen these estimates for the special case of a
symmetric problem. Numerical results provide a direct comparison with former
approaches and quantify the superiority of the new developed error bounds in
practice: Effectivities now decrease significantly; consequently, the proposed
methods provide accurate reduced basis approximations at much less
computational cost.
