The system-level size measures are particularly important in software project management as tasks such as planning and estimating the cost and schedule of software development can be performed more effectively when a size estimate of the entire system is available. However, due to the black-box nature of components, traditional software measures are not adequate as system-level measures for Component-Based Systems (CBS). Thus, if a system-level size is required, alternate measures should be used for sizing CBS. In this paper, we present a Function Point like approach, named Component Point to measure the system-level size of a CBS using the CBS specification written in UML. The Component Point approach integrates two software measures and extends an existing size measure from the more matured Object-Oriented paradigm to the related and relatively young CBS discipline. We also suggest a customized set of General System Characteristics so as to make our measure more relevant to CBS.