The end of Moore's law and Dennard scaling is shifting the typical computing paradigm towards Approximate Computing. This paper aims to explain an enhanced version of the MESI(Modified Exclusive Shared Invalid) cache coherence protocol using approximation and verifying its correctness with a model checker. In this proposed MESI-A(MESI-APPROX) cache coherence protocol, we subdivide the data into two parts: an approximate and precise one. By ignoring coherence communication for approximate data, the proposed model gains performance and saves energy. We formally verified MESI and MESI-A protocol using LTL (Linear Temporal Logic) and PCTL (Probabilistic Computational Tree Logic) specifications. On PARSEC 3.0 (Princeton Application Repository for Shared-Memory Computers) benchmark suite using TEJAS (The Efficient Java-Based Architectural Simulator), the improved protocol is performing efficiently with 5 per cent to 20 per cent approximated data with various applications. The energy gain is in correlation with the application's nature, but every application shows significant improvement.