Today's computing architectures and device technologies are becoming incapable of meeting the increasingly stringent demands on energy and performance posed by evolving applications. Therefore, alternative novel post-CMOS computing architectures are being explored. Some of these are Computationin-Memory (CIM) architectures based on memristive devices; they integrate the processing units and the storage in the same physical location (i.e., the memory based on memristive devices). Due to their advanced manufacturing processes, use of new materials, and dual functionality, testing such chips requires specific schemes and therefore special attention. This paper describes the need for testing CIM architectures, proposes a systematic test approach, and shows the strong dependency of the test solutions on the nature of the architecture. All of these will be demonstrated using a design that is designed for computationin-memory bit-wise logical operations.