This paper investigates the impact of non-line-of-site (NLOS) and multipath signals on frequency-locked loops (FLLs), which are commonly used to obtain Doppler shift measurements for velocity estimation in radio navigation. First, we use theory to model the effects of NLOS signals on the Doppler estimate produced by a conventional FLL with an arctangent discriminator. Next, we use experiments to verify theoretical predictions. A salient result is that, in the absence of a direct signal, a single NLOS signal does not corrupt Doppler observables if the angle-of-arrival (AOA) is known. Another striking result is that, in a multipath environment involving two signals, the arctangent discriminator (averaged over the beat frequency) tracks only the higher amplitude signal. Our investigation has particular significance for radio navigation in urban environments, either using global navigation satellite system (GNSS) signals or ground-based cellular signals.