Numerical simulation of the input impedance of wind instruments is the basis of much work in music acoustics. However, the accuracy and reproducibility of such simulations across different contributors remain little documented. This study aims to benchmark the reliability of numerical simulations for pipe impedance, focusing on simple geometries such as cylindrical and conical pipes, and to identify key factors influencing simulation variability. A collaborative approach was adopted, involving multiple contributors employing various numerical models, including TMM, FEM (1D or 3D), etc., and eventually different physical models for the propagation, the boundary conditions, and the thermo-viscous effects. Significant variability in simulation results was observed due to differences in implementation, numerical precision, and boundary condition modelling. Incomplete convergence in some methods also contributed to discrepancies. Despite these challenges, the collaborative work and exchanges reduced variability and improved consistency across contributors. The study highlights the importance of such benchmark and the interest to adopt good practices including verification of the numerical tools through comparative analysis and identification of convergence criteria. This work provides a framework for improving the reproducibility an accuracy of numerical simulations in musical acoustics context.