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Co-simulation is widely used in the industry due to the emergence of modular dynamical models made up of interconnected, black-boxed systems. Several co-simulation algorithms have been developed, each with different properties and different levels of accuracy and robustness. Among them, the most accurate and reliable ones are the iterative ones, although they have a main drawback in common: the involved systems are required to be capable of rollback. The latter denotes the ability of a system to integrate over a co-simulation time step that has already been simulated. Non-rollback-capable system can only go forward in time and every integrated step is definitive. In practice, the industrial modelling and simulation platforms rarely produce rollback-capable systems. This paper proposes a solution that slightly changes the co-simulation methodology and that enables to use iterative co-simulation methods on a modular model which contains non-rollback-capable systems in case the latter represent ordinary differential equations. The idea is to replace such a system by a simplified version, which is used to estimate the results of the integrations instead of integrating the real system. Once the co-simulation method's surrogate iterations on these estimators predict the convergence on the co-simulation step, the non-rollback-capable systems genuinely integrate the step using the estimated solution on the other systems before moving forward, transforming the iterative co-simulation method into a non-iterative one.