Muons have proven to be excellent probes of new physical phenomena, but theprecision of traditional curvature-based measurements of their energy degradesat high energies. Recent work has shown the feasibility of a new avenue for theprecise estimation of high-energy muons by exploiting the pattern of energy lossesin a dense, finely segmented calorimeter using convolutional neural networks(CNNs). However, CNN predictions of the muon energy suffered from significantbias, which hampers the reliability of traditional methods for quantifying theuncertainty of the estimates. Indeed, to date, there is no known solution to thegeneral problem of producing reliable uncertainty estimates of internal parametersof a statistical model from point predictions. In this paper, we propose WALDO,a new method that reframes the Wald test and uses the Neyman construction toconvert point predictions into valid confidence sets. We show that WALDO achievesconfidence sets with correct coverage regardless of the true muon energy value,while leveraging predictions from a CNN over a high-dimensional input space. Inaddition, we show that despite an increasing dimensionality, WALDO is able toextract useful information from a finer segmentation of the calorimeter, yieldingsmaller confidence sets, and hence more precise estimates of the muon energies.