The contribution presents the verification of the methodology of accelerated creep tests from the point of view of obtaining more information about the stress–strain behaviour of the investigated materials using the Digital Image Correlation method. Creep tests are performed on SAC305 and SACX0807 lead-free solders and are supplemented by numerical modelling using the finite element method, considering the viscoplastic model based on the theory of Perzyna, Chaboche, and Norton. The stress–strain behaviour of both solders appears to be very similar at applied strain rates of 0.0002–0.0026%/s and applied creep stresses of 15–28 MPa. Initially, the viscoplastic model is calibrated using an analytical approach. Then, the finite element model updating approach is used to optimise the material parameters based on the simultaneous simulations of creep and tensile tests. As a result, the total objective function value is reduced almost five times due to optimisation. The proposed type of accelerated test with an hourglass specimen proves to be suitable for calibrating the considered class of viscoplastic models. The main benefit is that a single specimen is required to obtain creep curves on various stress levels.