Our work is motivated by an important network design application in computational sustainability concerning wildlife conservation. In the face of human development and climate change, it is important that conservation plans for protecting landscape connectivity exhibit certain level of robustness. While previous work has focused on conservation strategies that result in a connected network of habitat reserves, the robustness of the proposed solutions has not been taken into account. In order to address this important aspect, we formalize the problem as a node-weighted bi-criteria network design problem with connectivity requirements on the number of disjoint paths between pairs of nodes. While in most previous work on survivable network design the objective is to minimize the cost of the selected network, our goal is to optimize the quality of the selected paths within a specified budget, while meeting the connectivity requirements. We characterize the complexity of the problem under different restrictions. We provide a mixed-integer programming encoding that allows for finding solutions with optimality guarantees, as well as a hybrid local search method with better scaling behavior but no guarantees. We evaluate the typical-case performance of our approaches using a synthetic benchmark, and apply them to a large-scale real-world network design problem concerning the conservation of wolverine and lynx populations in the U.S. Rocky Mountains (Montana).