In real-world decision-making scenarios, negative consequences do not always occur immediately after a choice. This delay between action and outcome drives the underestimation, or “delay discounting,” of punishment. While the neural substrates underlying sensitivity to immediate punishment have been well-studied, there has been minimal investigation of delayed consequences. Here, we assessed the role of lateral orbitofrontal cortex (LOFC) and basolateral amygdala (BLA), two regions implicated in cost/benefit decision-making, in sensitivity to delayed versus immediate punishment. The delayed punishment decision-making task (DPDT) was used to measure delay discounting of punishment in rodents. During DPDT, rats choose between a small, single-pellet reward and a large, three-pellet reward accompanied by a mild foot shock. As the task progresses, the shock is preceded by a delay that systematically increases or decreases throughout the session. We observed that rats avoid choices associated with immediate punishment, then shift preference toward these options when punishment is delayed. LOFC inactivation did not influence choice of rewards with immediate punishment, but decreased choice of delayed punishment. We also observed that BLA inactivation reduced choice of delayed punishment for ascending but not descending delays. Inactivation of either brain region produced comparable effects on decision-making in males and females, but there were sex differences observed in omissions and latency to make a choice. In summary, both LOFC and BLA contribute to the delay discounting of punishment and may serve as promising therapeutic targets to improve sensitivity to delayed punishment during decision-making.