Norming subspaces of Banach spaces

We show that if $ X$ is a closed subspace of a Banach space $ E$ and $ Z$ is a closed subspace of $ E^*$ such that $ Z$ is norming for $ X$ and $ X$ is total over $ Z$ (as well as $ X$ is norming for $ Z$ and $ Z$ is total over $ X$), then $ X$ and the preannihilator of $ Z$ are complemented in $ E$ whenever $ Z$ is $ w^*$-closed or $ X$ is reflexive.