Delay differential equations (DDEs) arise naturally as models of, ao, networked control systems, where the communication delay in the feedback loop cannot always be ignored. Such delays can eg prompt oscillations in otherwise stable feedback loops and thus cause severe deterioration of control performance, invalidating both stability and safety properties. Despite the omnipresence of feedback delays, stateexploratory automatic verification methods have until now concentrated on ordinary differential equations (and their piecewise extensions to hybrid state) only, failing to address the effects of delays on system dynamics. We overcome this problem by iterating bounded degree interval-based Taylor overapproximations of the time-wise segments of the solution to a DDE, thereby identifying and automatically analyzing the operator that yields the parameters of the Taylor overapproximation for the next temporal segment from the current one. By using constraint solving for analyzing the properties of this operator, we obtain a procedure able to provide stability and safety certificates for a simple class of DDEs.