2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/100965We prove Gronwall-type estimates for the distance of integral curves of smooth vector fields on a Riemannian manifold. Such estimates are of central importance for all methods of solving ODEs in a verified way, i.e., with full control of roundoff errors. Our results may therefore be seen as a prerequisite for the generalization of such methods to the setting of Riemannian manifolds.4 pages, 1 figure, correction of some misprintsDifferential GeometryClassical Analysis and ODEs53B21; 53C22; 34A26text