A known source of error in noise figure characterization is the variation of the device characteristics within the bandwidth of the instrument receiver. In this paper, an in-depth analysis of the effect of the receiver bandwidth on noise figure characterization accuracy is developed. For the first time, comparative results for Y-factor and cold-source techniques are given. The analysis clarifies some contradictions about the origin and the final impact of bandwidth effects in Y-factor. In addition, effects derived from an excessively wide bandwidth of the noise receiver are shown to be completely different in both techniques, being more critical in cold-source. As a result of the analysis, correction terms are provided for those cases in which receivers with narrow enough bandwidths are not available. The conclusions extracted from the theoretical formulation are confirmed by the measurements carried out on several narrow-band devices under tests with different characteristics.