The relative displacements between the girders and piers of isolated bridges during intense earthquakes are usually so large that traditional restrainers cannot accommodate the resulting deformation. A novel superelastic shape memory alloy (SMA) honeycomb damper (SHD) is proposed as a means to combine the large strain capacity of SMA and the geometrical nonlinear deformation of honeycomb structures. As a result, the large deformation capacity of the novel damper satisfies the requirements for bridge restrainers. The proposed device consists of a superelastic shape memory alloy (SMA) honeycomb structure, which enables a self-centering capability, along with steel plates that serve to prevent the buckling of the SMA honeycomb. An examination of the SHD was undertaken initially from theoretical perspectives. A multi-cell SHD specimen was subsequently manufactured and evaluated. Following this, numerical simulation analyses of the SHDs using a three-dimensional high-fidelity finite element model were employed to examine the experimental results. In the end, a technique for improving the SHD was suggested. The results indicate that the SHD is able to demonstrate superior self-centering capabilities and stable hysteretic responses when subjected to earthquakes.