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Perception is fallible. Humans know this, and so do some nonhuman animals like macaque monkeys. When monkeys report more confidence in a perceptual decision, that decision is more likely to be correct. It is not known how neural circuits in the primate brain assess the quality of perceptual decisions. Here, we test two hypotheses. First, that decision confidence is related to the structure of population activity in the sensory cortex. And second, that this relation differs from the one between sensory activity and decision content. We trained macaque monkeys to judge the orientation of ambiguous stimuli and additionally report their confidence in these judgments. We recorded population activity in the primary visual cortex and used decoders to expose the relationship between this activity and the choice-confidence reports. Our analysis validated both hypotheses and suggests that perceptual decisions arise from a neural computation downstream of visual cortex that estimates the most likely interpretation of a sensory response, while decision confidence instead reflects a computation that evaluates whether this sensory response will produce a reliable decision. Our work establishes a direct link between neural population activity in the sensory cortex and the metacognitive ability to introspect about the quality of perceptual decisions.