Perception is uncertain. Repeated presentations of the same stimulus elicit variable perceptual impressions. To robustly guide behavior, the neural circuits that mediate perception must therefore extract both feature estimates and feature uncertainty from sensory inputs. How they do so is not well understood. We addressed this question using an approach that combines three components. First, a rich stimulus set which varies in feature value and uncertainty. Second, observation of neural population activity in a sensory circuit that represents these features. And third, a maximum likelihood decoder of neural activity, tasked to estimate feature value and uncertainty on each trial. We took this approach to macaque primary visual cortex (V1), where neural activity encodes local image orientation. We made extracellular recordings of V1 population activity and described each neuron’s responses with a stimulus-response model built from operations of linear filtering, nonlinear transduction, gain control, and a doubly stochastic noise process. We then used this model to derive the maximum likelihood estimator of stimulus orientation. Orientation estimates were on average unbiased, even in the presence of nuisance variation (contrast and spread). On individual trials, orientation estimation error tended to be small for high contrast, small spread stimuli, but could be substantial when contrast was low, or spread was high. This was reflected in the uncertainty estimates of the decoder, which we obtained by computing the width of the orientation likelihood function. We then asked which aspect of neural activity distinguishes uncertain from certain trials. We identified two candidate representations. First, the overall level of activity (the higher the population firing rate, the more precise the orientation estimate). And second, a model-based estimate of variability in response gain (the higher this variability, the less precise the orientation estimate). Our findings clarify how sensory circuits jointly encode stimulus features and their uncertainty.