A method is presented for deterministic global optimization in the estimation of parameters in models of dynamic systems. The method can be implemented as an epsilon-global algorithm or, by use of the interval-Newton method, as an exact algorithm. In the latter case, the method provides a mathematically guaranteed and computationally validated global optimum in the goodness-of-fit function. A key feature of the method is the use of a new validated solver for parametric ordinary differential equations (ODEs), which is used to produce guaranteed bounds on the solutions of dynamic systems with interval-valued parameters, as well as on the first- and second-order sensitivities of the state variables with respect to the parameters. The computational efficiency of the method is demonstrated using several benchmark problems.