This paper highlights the need to meet both Grid user and resource provider security requirements, describing the rationale for securing Grid workflows: a set of tasks arranged into a logical order to process a Grid user's dataset. An overview of a secure protocol using Trusted Computing technology is provided, which is further enhanced with platform virtualisation hardware and software. The proposed scheme allows the selection of trustworthy resource providers and gives confidentiality and integrity protection to the workflow, the Grid user's processes and data. The scheme also detects any problems during workflow execution, collecting information that can be used for process provenance.