As the technology node advances into the nanometer era, via-open defects are one of the dominant failures. To improve via yield and reliability, redundant-via insertion is a highly recommended technique proposed by foundries. Traditionally, double-via insertion is performed at the post-layout stage. The increasing design complexity, however, leaves very limited space for post-layout optimization. It is thus desirable to consider the double-via insertion at both routing and post-routing stages. In this paper, we present a new full-chip gridless routing system considering doublevia insertion for yield enhancement. To fully consider double vias, the router applies a novel two-pass, bottom-up routability-driven routing framework. We also propose a new post-layout doublevia insertion algorithm to achieve a higher insertion rate. Based on a bipartite graph matching formulation, we develop an optimal double-via insertion algorithm for the cases with up to three routing layers and the stack-via structure, and then extend the algorithm to handle the general cases. Experiments show that our methods significantly improve the via count, the number of dead vias, double-via insertion rates, and running times.