Service-based Grid infrastructures emphasize service composition rather than sharing of low level resources. The idea is to build Grid applications out of computational services provided by the different sites of the Grid. Recent developments in the area of Web services have strengthened this idea by standardizing procedures like service description, publication and invocation. What is still missing is the infrastructure necessary to support the complete life cycle of applications running on service based Grids, i.e., suitable programming paradigms, execution infrastructure, and the ability to monitor and control such computations. Moreover, once computations are made of composable services, dependability becomes a key issue that needs to be addressed by the infrastructure as it cannot be addressed separately by each individual service. To address these concerns, we have developed the BioOpera Grid computing platform. BioOpera is a process support system for dependable cluster computing that has been extended with additional functionality to provide adequate support for service-based Grids. In this paper we describe how BioOpera can be used to develop, execute, and administer highly dependable computations over service-based Grids.