The inadequate level of reactive power generation by distributed energy resources (DERs) in extreme conditions could render networked microgrids (NMGs) more susceptible to major contingencies. In extreme conditions when the NMGs islanding from the main grid might occur, the inadequacy of reactive power generation could make it more difficult for NMGs operators to maintain a reasonable margin for the resilient NMGs operation. This paper studies the resilient reactive power scheduling of NMGs in extreme conditions. A two-stage model is proposed which applies Here-And-Now (HAN) and Wait-And-See (WAS) decisions at the first and the second stages, respectively. The HAN and WAS stages are linked through a stochastic programming approach where the entire problem is formulated in mixed-integer linear programming. To address scalability and privacy concerns in NMGs operations, the proposed two-stage model is decentralized and decomposed into a master problem and three subproblems and linked by Benders cuts. The master problem identifies the least-cost operation plan for NMGs considering normal and extreme conditions at Stages 1 and 2. Subproblems I, II, and III satisfy the feasibility, security, and optimality of individual microgrid operations, respectively. The DER limitations in supplying reactive loads are more evident at Stage 2 during the islanding simulation, which is managed by the proposed extreme condition reactive power procurement approach. The effectiveness of proposed two-stage model in enhancing the resilience of the NMGs is assured by comprehensive simulation studies.