The efficient solution of a class of controller approximation problems by using frequency-weighted balancing related model reduction approaches is considered. It is shown that for certain standard performance and stability enforcing frequency weights, the computation of the frequency-weighted controllability and observability grammians can be done by solving reduced order Lyapunov equations regardless the controller itself is stable or unstable. The new approach can be used in conjunction with accuracy enhancing square-root and balancing-free techniques recently developed by the authors for the frequency-weighted balancing related model reduction.