Calibrating a car-following model is an essential component in the traffic load analysis of bridges, since the parameter set fundamentally determines the spatiotemporal distributions of the vehicles and the magnitude of the load effects. In bridge engineering, car-following models are adapted from transportation engineering so that they do not consider load effects in the calibration process. This paper proposes a novel framework that factors vehicle motions and load effects into a multi-objective optimisation problem to calibrate car-following models. The Intelligent Driver Model (IDM) and the Gipps’ model are introduced for comparison. In the testing, three different types and spans of bridges are selected to compare the models in terms of fitness, robustness, and compactness of the solution. Within the proposed framework, the Gipps’ model proves to be superior in terms of fitness but achieves poor performance in robustness, while the IDM exhibits the opposite pattern. The solution compactness of the Gipps’ model improves with higher truck weights only in the circumstance of the load effects type with a unimodal influence line. Overall, the Gipps’ model is recommended for analysis with abundant data. Otherwise, the IDM can be adopted for a non-optimal but robust result.