We predict a sequence of magic-zero wavelengths for the Sr excited 5s5p P-3(0) state, and provide a general roadmap for extracting transition matrix elements using precise frequency measurements. We demonstrate that such measurements can serve as a global benchmark of the spectroscopic accuracy that is required for the development of high-precision predictive methods. These magic-zero wavelengths are also needed for state-selective atom manipulation for implementation of quantum logic operations. We also identify five magic wavelengths of the 5s(2) S-1(0)-5s5p P-3(0) Sr clock transition between 350 and 500 nm which can also serve as precision benchmarks.