We report on a mechanization in the Coq proof assistant of the decidability of conversion and type-checking for Martin-Löf Type Theory (MLTT), extending a previous Agda formalization. Our development proves the decidability not only of conversion, but also of type-checking, using bidirectional derivations that are canonical for typing. Moreover, we wish to narrow the gap between the object theory we formalize (currently MLTT with Π, Σ, N and one universe) and the metatheory used to prove the normalization result, e.g., MLTT, to a mere difference of universe levels. We thus avoid induction-recursion or impredicativity, which are central in previous work. Working in Coq, we also investigate how its features, including universe polymorphism and the metaprogramming facilities provided by tactics, impact the development of the formalization compared to the development style in Agda. The development is freely accessible on GitHub [2].