Worst-case execution time (WCET) estimation tools are complex pieces of software performing tasks such as computation on control flow graphs (CFGs) and bound calculation. In this paper, we present a formal verification (in Coq) of a loop bound estimation. It relies on program slicing and bound calculation. The work has been integrated into the CompCert verified C compiler. Our verified analyses directly operate on non-structured CFGs. We extend the CompCert RTL intermediate language with a notion of loop nesting (a.k.a. weak topological ordering on CFGs) that is useful for reasoning on CFGs. The automatic extraction of our loop bound estimation into OCaml yields a program with competitive results, obtained from experiments on a reference benchmark for WCET bound estimation tools.