The damage of finger electrodes of surface acoustic wave (SAW) structures due to material transport (acoustomigration) forming voids and hillocks is strongly associated with the SAW stress field, the temperature and properties of the fingers material and their configuration. By application of Cu thin films a significant higher performance of SAW structures with respect to power durability, reliability and lifetime is obtained. In the present paper Cu finger electrodes of a special power SAW test structure were fabricated in trenches of STX quartz substrates using the copper damascene technique. In comparison with conventional finger electrodes located on the substrate surface, such an embedded structure enables some new features regarding their acoustical and acoustomigration behavior. So high power SAW load cannot cause fatal failures by shorts between adjacent fingers. This fact is specially important for SAW devices in the GHz range. The trench structuring into the substrate was carried out by reactive ion (RIE) or ion beam etching (IBE) technique using a metallic hard mask. Etched trenches were filled with a conductive Ta-Si-N / Cu-layer system by magnetron sputtering in a cluster tool, and structured by a chemical-mechanical polishing (CMP) process. Subsequently, after cleaning an insulating Ta-based barrier (system Ta-Si-O / Ta-Si-N) layer was deposited on the wafer surface. This covering layer also acts as a protective coating. Such a metallization system enables sufficient bonding properties using Al-wires. First results of electrical measurements show that travelling SAW could be excited in quartz substrates.