The demand for high-frequency low-loss filters generates intensive research on innovative wave guide solutions. In this work, a GHz SAW device based on a ZnO/Si structure was fabricated using classical UV photolithography. The thickness of the piezoelectric thin film was optimized and a specific interdigital transducer structure was used to generate third and fifth harmonic guided waves at 2.5 GHz and 3.5 GHz, respectively, with an aluminum strip larger than 1 micrometer. Different modes have been measured and theoretically identified thanks to an advanced finite-element/boundary-elementbased model. Good agreement is found between theory and experiments. The high-frequency modes have been fully characterized, allowing for accurate design of SAW devices exploiting such modes.