Gallium nitride (GaN) is a robust piezoelectric semiconductor with excellent thermal and chemical stability, making it an attractive material for surface acoustic wave (SAW) sensors operating in high temperature and harsh environments. The sensitivity of SAW devices is proportional to the square of the operating frequency. Therefore, high operating frequencies into the GHz regime are desirable for SAW sensors. For GaN, this requires sub-micron interdigital transducers (IDTs) when devices are designed to operate at the fundamental Rayleigh mode frequency. The necessity for sub-micron IDTs can increase fabrication costs and complexity. By designing SAW devices to operate at harmonic frequencies, GHz operation can be realized with relatively large IDTs, resulting in simpler and more cost effective solutions for GaN based SAW sensors. Devices have previously been designed to operate at the 5th and higher harmonics on lithium niobate, but there are no reports of using this technique on GaN in the literature. In this study, GaN thin films have been grown via metal organic vapor phase epitaxy on sapphire substrates. SAW devices designed to operate at the fundamental frequency and higher harmonics have been fabricated and measured. Operating frequencies greater than 2 GHz have been achieved using IDTs with 5 μm fingers. In addition, reduction of electromagnetic feedthrough around the 5th and 7th harmonic is demonstrated through varying ground electrode geometries.