Vibration-based sound power (VBSP) measurement methods are appealing because of their potential versatility in application compared to sound pressure and intensity-based methods. It has been understood that VBSP methods have been reliant on the acoustic radiation resistance matrix specific to the surface shape. Expressions for these matrices have been developed and presented in the literature for flat plates, simple-curved plates (constant radius of curvature in one direction), and cylindrical- and spherical-shells. This paper shows that the VBSP method is relatively insensitive to the exact form of the radiation resistance matrix and that computationally efficient forms of the radiation resistance matrix can be used to accurately approximate the sound power radiated from arbitrarily curved panels. Experimental sound power measurements using the VBSP method with the simple-curved plate radiation resistance matrix and the ISO 3741 standard method are compared for two arbitrarily curved panels and are shown to have good agreement. The VBSP method based on the simple-curved plate form of the radiation resistance matrix is also shown to have excellent agreement with numerical results from a boundary element model, which inherently uses the appropriate form of the radiation resistance matrix.