The use of component-based software has become more and more important in state-of-the-art and state-of-the-practice of software and system development. Using COTS software promises faster time-to-market, which can yield substantial advantages over competitors with regards to earlier placement of a new product on a market. At the same time, component-based software introduces risks such as unknown quality properties of the components in use that can inject harmful side effects into the final product. This paper proposes a multidimensional classification scheme for assessing component-based systems. The classification scheme provides insight into what quality characteristics, managerial features, or assessment methods and techniques might be used for evaluating different component artefacts.