The film bulk acoustic resonator (FBAR) is a widely-used MEMS device which can be used as a filter, or as a gravimetric sensor for biochemical or physical sensing. Current device architectures require the use of an acoustic mirror or a freestanding membrane and are fabricated as discrete components. A new architecture is demonstrated which permits fabrication and integration of FBARs on arbitrary substrates. Wave confinement is achieved by fabricating the resonator on a polyimide support layer. Results show when the polymer thickness is greater than a critical value, d, the FBARs have similar performance to devices using alternative architectures. For ZnO FBARs operating at 1.3-2.2 GHz, d is ~9 μm, and the devices have a Q-factor of 470, comparable to 493 for the membrane architecture devices. The polymer support makes the resonators insensitive to the underlying substrate. Yields over 95% have been achieved on roughened silicon, copper and glass.