The microscopic and macroscopic dynamics of calcium alkali nitrate melts are studied in their supercooled regime by means of shear rheology and nuclear magnetic resonance (NMR). The structural relaxation is probed using shear rheology to access the viscoelastic flow as well as using physical aging experiments. By exploiting the strongly quadrupole-perturbed 87Rb nucleus, the local dynamics is probed on the milliseconds to nanoseconds range using various NMR methods involving central-transition stimulated-echo techniques, line shape analyses, spin relaxations, and second-order dynamic shift effects. The time scales monitored via the local Rb probe are in harmony with the electrical conductivity relaxation times. The low-temperature NMR line shapes agree excellently with those predicted by the Czjzek model. The temperature dependent second-order dynamic frequency shift is described using the imaginary part of the spectral density. It is demonstrated how the latter quantity can be generalized to include effects of correlation time distributions.