The power grid needs to ensure demand-supply balance at all times and locations, subject to generation and transmission constraints.  The uncertainty associated with high renewable penetration poses new challenges to such a reliability requirement.  We demonstrate that existing two-stage methods in the literature, which assume that uncertainty is completely revealed at a second stage, fail to account for the online sequential nature of the decisions, and therefore may significantly under-estimate the resource requirement for reliability under high renewable uncertainty. Through the notion of ``safe dispatch sets,'' we show that both the day-ahead  reliability assessment decisions and the real-time dispatch decisions can be made in an online manner to provably guarantee grid reliability under a given level of future uncertainty.  However, in general such safe dispatch sets may be difficult to compute.  We then develop low-complexity characterizations of the safe dispatch sets, first for a simpler single-bus two-generator
setting, and then for general multi-bus settings.