This note addresses the problem of instability in both model and controller reduction methods based on similarity transformations. For a given model (controller) a general framework is proposed that parameterizes a large set of reduced models (controllers) that preserve the stability of the original model (closed loop system). In addition, a sufficient condition for the existence of such a framework is derived. As an application of the main results, it is shown how different reduction methods can be modifed, if they fail to maintain stability.