In the last years, many computational models have been developed for tensile fracture in concrete. However, their reliability is related to the correct estimate of the model parameters, not all directly measurable during laboratory tests. Hence, the development of inverse procedures is needed, that provides the parameters estimate minimizing, iteratively, the discrepancy between experimental and computational data. The present research focuses on the identification of the length scale parameter and the slope of the softening branch of the stress-strain constitutive law of the gradient-enhanced continuum damage model. Various issues related to the forward model and to the inverse problem are analyzed: the well-posedness of the inverse problem (influenced by quality and quantity of the chosen experimental data), the choice of the adopted inverse strategy (as an effective, efficient and robust searching scheme) and the assessment of the predictive capabilities of the so-calibrated numerical model related to size and loading condition effects. For this purpose the results of four experimental series are considered: i) cable-loaded uniaxial tensile tests on single-edge notched sandstone specimens [1] ii) tensile size effect tests on concrete dog-bone shaped specimens [2] [3] iii) three-point bending tests on notched concrete beams [4] and iv) double-edge notched uniaxial tensile tests and single-edge notched bending tests on specimens made of the same concrete [5] [6]. The developed inverse strategy is based on two techniques in cascade: the K-Nearest Neighbors method and the Kalman filter method. The first method provides a preliminary study of the parameters space, while the second represents a refining searching technique that takes into account the uncertainties related to the experimental data and to the model parameters estimate. The results show that considering only global force-displacement curves of one single specimen size or of different specimen sizes, the uniqueness and/or stability of the inverse solution are not guaranteed. Additional local data, such as the evolution of the width of the fracture process zone during the fracture process, are needed to recover the well-posedness of the inverse problem. Moreover, using only a single parameter set for all specimen sizes, the analyzed computational model can reproduce size effect phenomena that are less pronounced with respect to the ones obtained in the experiments.