Components (in-house or pre-fabricated) are increasingly being used to reduce the cost of software development. Given that these components may not have not been developed with dependability as a driver, the components need to be adapted to deal with errors coming from their environment. To achieve this, error containment wrappers are often added to increase the robustness of such components. Adopting a gray-box perspective of software, we first present a modular approach for specifying and verifying embedded software made from components, based on concepts from category theory. This modular approach allows the system designer to check for semantic compatibility. To generate the error containment wrappers needed for adaptation, we subsequently present an algorithm that systematically generates the required wrappers. Using the information obtained through wrapper design, we develop an approach to identify relevant test cases to test individual components. We further exploit the modularity of the specification to identify the relevant test cases to perform testing at different levels of SW abstraction.