Microgrids are resources that can be used to restore critical loads after a natural disaster, enhancing resilience of a distribution network. To deal with the stochastic nature of intermittent energy resources, such as wind turbines (WTs) and photovoltaics (PVs), many methods rely on forecast information. However, some microgrids may not be equipped with power forecasting tools. To fill this gap, a risk-limiting strategy based on measurements is proposed. Gaussian mixture model (GMM) is used to represent a prior joint probability density function (PDF) of power outputs of WTs and PVs over multiple periods. As time rolls forward, the distribution of WT/PV generation is updated based the latest measurement data in a recursive manner. The updated distribution is used as an input for the risk-limiting load restoration problem, enabling an equivalent transformation of the original chance constrained problem into a mixed integer linear programming (MILP). Simulation cases on a distribution system with three microgrids demonstrate the effectiveness of the proposed method. Results also indicate that networked microgrids have better uncertainty management capabilities than stand-alone microgrids.