Regulation of DC microgrid voltage in presence of variable sources and loads is quite challenging. The ability of a microgrid to pay off the critical loads when subjected to disturbances, such as utility grid outage/poor climatic conditions, has gained importance recently. To address the above issues, we propose a resiliency analysis of a DC microgrid interconnected with 400 V and 200 V buses. The interconnected microgrid system is fed with solar PV along with the energy storage system and is integrated with a utility grid. Boost and high step-up DC-DC converters are employed for DC bus voltage regulation with droop index control. Here, the droop coefficient is optimized using particle swarm optimization (PSO) while maintaining uninterrupted service to critical loads and for satisfactory voltage regulation. The effectiveness of the droop index control method is tested in comparison to other optimization techniques and also with the conventional method. The resiliency analysis of the overall system, aiming for continuous power supply to the critical loads while maintaining the grid voltage unaffected, is carried out in grid outage, low solar insolation, and grid restoration conditions. The reliability of the interconnected DC microgrid test system is evaluated using the loss of power supply probability index for normal, grid outage, and grid restoration conditions. The system is implemented using PSCAD/EMTDC platform. Finally, the experimental prototype of a high step-up DC-DC converter is developed and tested to validate the effectiveness of the droop index controller with an optimized droop coefficient.