Meaningful exchange of data or services with a software unit requires identifying and satisfying its conceptual constraints. Otherwise, unexpected conceptual mismatches lead to late projects and costly rework. However, for blackbox software providers, it is unguided and time-consuming task to share the conceptual constraints explicitly with third-party clients who also lack the guidance on detecting the conceptual mismatches. To cope with these challenges, we built a Conceptual Interoperability Constraints (COINs) model, which is the base for our Conceptual Interoperability Analysis (COINA) framework. COINA helps architects and analysts to identify the conceptual constraints and mismatches of software units effectively and efficiently. It comprises: (1) Proactive, semi-automatic, in-house preparation for interoperable units that helps providers to share the conceptual constraints with the least effort. (2) A systematic, algorithm-based method for mapping conceptual constraints of systems to detect their mismatches. A multi-run controlled experiment confirmed our hypotheses that our approach significantly increases the effectiveness and efficiency in detecting conceptual mismatches.