To accurately model double-stranded DNA in a manner that is computationally efficient, coarse-grained models of DNA are introduced, where model parameters are selected by fitting the spectrum of observable DNA knots: We develop a general method to fit free parameters of coarse-grained chain models by comparing experimentally obtained knotting probabilities of short DNA chains to knotting probabilities that are computed in Monte Carlo simulations, resulting in coarse-grained DNA models which are tailored to reflect DNA topology in the best possible way. The method is exemplified by fitting ideal chain models as well as a bead-spring model with excluded volume interactions, to model double-stranded DNA for physiological as well as for high salt concentrations. The resulting coarse-grained DNA models predict the correct persistence length and effective diameter of double-stranded DNA, and can in principle be used for dynamical investigations using Molecular Dynamics. Our modelling ansatz thus provides a blueprint for building coarse-grained models of polymers, which are solely based on knotting spectra.