Reserve deliverability refers to the ability of power system reserves to be deployed and without violating transmission constraints. Reserve procurement enhancement (RPE) constraints, which capture post reserve deployment power flow under contingency events, can be incorporated in the dispatching models to improve reserve deliverability. However, modeling all generator contingencies within RPE constraints in real-world electricity markets significantly increases the optimization problem's complexity and is not scalable. The combination of generator failures, reserve deployment in response, and net load deviation generates numerous scenarios. To address this, the Umbrella Contingency Set (UCS) is used to represent a subset of credible contingencies that is sufficient to achieve security and economic performance levels equivalent to, or very close to, those attained when considering all credible contingencies. This study proposes a novel approach utilizing robust optimization to identify the UCS, focusing on the worst-case scenario derived from a combination of events, reserve deployment, and net load uncertainty. Case studies conducted on the IEEE RTS 24-bus system and a synthetic Electric Reliability Council of Texas (ERCOT) system demonstrate the effectiveness of the approach in enhancing reserve deliverability and mitigating violations under various levels of net load uncertainty while ensuring computational tractability.