We consider shielding critical links to enhance the robustness of a network, in which shielded links are resilient to failures. We first study the problem of increasing network connectivity by shielding links that belong to small cuts of a network, which improves the network reliability under random link failures. We then focus on the problem of shielding links to guarantee network connectivity under geographical and general failure models. We develop a mixed integer linear program (MILP) to obtain the minimum cost shielding to guarantee the connectivity of a single source-destination pair under a general failure model, and exploit geometric properties to decompose the shielding problem under a geographical failure model. We extend our MILP formulation to guarantee the connectivity of the entire network, and use Benders decomposition to significantly reduce the running time. We also apply simulated annealing to obtain near-optimal solutions in much shorter time. Finally, we extend the algorithms to guarantee partial network connectivity, and observe significant reduction in the shielding cost, especially when the geographical failure region is small.