Semantic Grids need to support dynamic service discovery - to enable users to look for services based on their properties. Such properties generally include the interface provided by a service (such as message types supported) - but may also include other non-functional properties - such as service performance and cost. This requires the provision and recording of metadata about a service that is not supported by current registry services such as UDDI. A framework to facilitate reputation-based service selection in Semantic Grids is presented. The proposed framework has two key features that distinguish it from other work in this area. First, an adaptive reputation-aware service discovery algorithm is provided. Second, a service-oriented distributed reputation assessment algorithm is presented. The main components of the framework are described.