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Certifying the output of tools solving complex problems so as to ensure the correctness of the results they provide is of tremendous importance. Despite being widespread for SAT-solvers, this level of exigence has not yet percolated for tools solving more complex tasks, such as model counting or knowledge compilation. In this paper, the focus is laid on a general family of top-down Decision-DNNF compilers. We explain how those compilers can be tweaked so as to output certifiable Decision-DNNF circuits, which are mainly standard Decision-DNNF circuits decorated by annotations serving as certificates. We describe a polynomial-time checker for testing whether a given CNF formula is equivalent or not to a given certifiable Decision-DNNF circuit. Finally, leveraging a modified version of the compiler d4 for generating certifiable Decision-DNNF circuits and an implementation of the checker, we present the results of an empirical evaluation that has been conducted for assessing how large are in practice certifiable Decision-DNNF circuits, and how much time is needed to compute and to check such circuits.