Most signal-to-noise ratio (SNR) estimators use the receiver matched filter output sampled at the symbol rate, an approach which does not preserve all information in the analog waveform due to aliasing. Thus, it is relevant to ask whether avoiding aliasing could improve SNR estimation. To this end, we compute the corresponding data-aided (DA) and nondata-aided (NDA) Cramér-Rao bounds (CRBs). We adopt a novel dual filter framework, which is shown to be information-preserving under suitable conditions and considerably simplifies the analysis. It is shown that the CRB can be substantially reduced by exploiting any available excess bandwidth, depending on the modulation scheme, the SNR range, and the estimator type (DA or NDA).