The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-23165-5_3This paper introduces the idea of using assertion checking for enhancing the dynamic slicing of Maude computation traces. Since trace slicing can greatly simplify the size and complexity of the analyzed traces, our methodology can be useful for improving the diagnosis of erroneous Maude programs. The proposed methodology is based on (i) a logical notation for specifying two types of user-defined assertions that are imposed on execution runs: functional assertions and system assertions; (ii) a runtime checking technique that dynamically tests the assertions and is provably safe in the sense that all errors flagged are definite violations of the sp...