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 SATsolvers, 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 the certifiable Decision-DNNF circuits that can be generated in practice, and how much time is needed to compute and to check such circuits.