The present paper derives highly dispersive soliton solutions in a coupler from optical metamaterials with Kerr law of nonlinear refractive index. In nonlinear optics and photonics, these wave packets possess a unique property, allowing them to sustain their shape and velocity during propagation through nonlinear media. Optical couplers utilizing metamaterials are advanced devices tailored to enhance the coupling and transfer of optical signals between different optical components or systems by harnessing the unique characteristics of these specially engineered materials. The paper's novelty lies in considering highly dispersive optical solitons that can be studied in optical couplers constructed from metamaterials. This paper’s primary goal is to integrate a governing model concerning highly dispersive solitons in optical couplers with the incorporation of metamaterials. Therefore, the unified Riccati equation expansion procedure and the enhanced Kudryashov’s scheme are adopted. They are being applied to such a device for the first time. These yield a full spectrum of optical solitons as well as straddled solitons. The novelty lies in the joint application of the two procedures, which uncovers various solitons. Furthermore, one of the approaches uncovers an unexpected benefit by revealing straddled soliton solutions.