Presenting cloud energy storage system (CESS) in the landscape of storage devices exposes microgrids (MGs) to a substantial change. Employing a specific type of inverter namely synchronverter as the connecting interface for CESS gains high inertial response in MGs with high penetration level of inverter-based distributed generations (IBDGs). However, high fault contribution of synchronverters can lead to challenging issues. Nevertheless, presence of fault resistance which results in malfunctioning of the recloser-fuse pair intensifies the cruciality of the dilemma. In this paper, at the outset, the effects of contribution of synchronverter-based CESS and also fault resistance on recloser-fuse protection are explored and then, a new algorithm is proposed for tackling these bottlenecks. To overcome these hurdles, the conventional recloser-fuse scheme is applied at first. Then, by using the obtained schemes for fast and slow operations of the recloser, a specific part of them is set in a manner that the fuse-saving task is performed properly even when the synchronverter-based CESS is deployed. On the other hand, the other part of the recloser scheme is altered in a way that the maloperation of the recloser-fuse pair owing to the fault resistance is alleviated. Adequate numerical analyses are conducted to evaluate the proposed scheme.