Bridges with cable systems, such as Nielsen–Lohse bridges, are designed to support loads by the tensile force of the cables. Therefore, the tension of cables should be verified during construction and maintenance. In Japan, cable tension is typically estimated using the higher-order vibration method based on the natural frequencies of the cables. Because the higher-order vibration method considers a single cable, all intersection clamps must be removed to apply this method to the cables of Nielsen–Lohse bridges, where several cables are connected by intersection clamps. However, the removal of intersection clamps is time-consuming. This paper proposes a cable tension estimation method that eliminates the need to remove intersection clamps by leveraging an approach based on the cable’s mode shape. Because the bending stiffness of cables correlates with cable corrosion, this study developed a method for simultaneously estimating tension and bending stiffness. The proposed method was validated through numerical simulations and model experiments. The numerical simulations revealed that tension was accurately estimated only when low-order modes were used. When low- to high-order modes were used, the proposed method enabled the simultaneous estimation of tension and bending stiffness with high accuracy. In the model experiments, the proposed method estimated tension and bending stiffness with a high accuracy within 5% when high-order modes were used. The proposed method is expected to eliminate the need to remove intersection clamps, leading to more efficient cable management and maintenance.