We investigate a new form of (privacy-preserving) inconsistency measurement for multi-party communication. Intuitively, for two knowledge bases \(K_A,K_B\) (of two agents A, B), our results allow to quantitatively assess the degree of inconsistency for \(K_A \cup K_B\) without having to reveal the actual contents of the knowledge bases. Using secure multi-party computation (SMPC) and cryptographic protocols, we develop two concrete methods for this use-case and show that they satisfy important properties of SMPC protocols—notably, input privacy, i.e., jointly computing the inconsistency degree without revealing the inputs.