The evaluation of software architectures is crucial to ensure that the design of software systems meets the requirements. We present a generic methodical framework that enables the evaluation of component-based software architectures. It allows to determine system characteristics on the basis of the characteristics of its constituent components. Basic prerequisites are discussed and an overview of different architectural views is given, which can be utilised for the evaluation process. On this basis, we outline the general process of evaluating software architectures and provide a taxonomy of existing evaluation methods. To illustrate the evaluation of software architectures in practice, we present some of the methods in detail.