  We present a Lohner-type algorithm for rigorous integration of systems of
Delay Differential Equations (DDEs) with multiple delays and its application in
computation of Poincar\'e maps to study the dynamics of some bounded, eternal
solutions. The algorithm is based on a piecewise Taylor representation of the
solutions in the phase-space and it exploits the smoothing of solutions
occurring in DDEs to produces enclosures of solutions of a high order. We apply
the topological techniques to prove various kinds of dynamical behavior, for
example, existence of (apparently) unstable periodic orbits in Mackey-Glass
Equation (in the regime of parameters where chaos is numerically observed) and
persistence of symbolic dynamics in a delay-perturbed chaotic ODE (the
R\"ossler system).
