Non-Fregean logics reject Frege’s Principle according to which sentences are names of their truth values. Instead, the non-Fregean framework assumes the existence of a universe of semantic correlates of sentences in the semantics and introduces into the language a non-truth-functional propositional connective of non-Fregean equivalence, \(\equiv \) , which enables referring to and reasoning about the denotations of sentences. It turns out that many non-classical logics – including modal, many-valued, intuitionistic, relevant, and paraconsistent logics – can be represented as non-Fregean systems. Thus, the non-Fregean approach offers a unified and inclusive framework for studying the nature of logical connectives and the principles underlying reasoning about the interplay between sentence meanings. Sentential Calculus with Identity ( \(\textsf{SCI}\) ) is a paradigmatic example of a classical non-Fregean logic. In the paper, we present a new, non-labelled dual tableau calculus for \(\textsf{SCI}\) , \(\textsf{DT}_\textsf{SCI}\) for which we prove soundness, completeness, and termination with an exponential bound on branch length. We compare \(\textsf{DT}_\textsf{SCI}\) with the already existing complexity-optimal labelled tableau calculus \(\textsf{T}_\textsf{SCI}\) . We show that even though these systems use very different methodologies, which manifests itself not only in the presence of labels in one of them and the lack thereof in the other, but also in disparate sets of rules handling the identity connective and dissimilar techniques used throughout the completeness proofs, both offer a satisfactory solution to the problem of satisfiability/validity of \(\textsf{SCI}\) -formulas.