This paper deals with the problem of H-infinity model reduction for linear continuous time-delay systems. For a given delay system, the problem we address is the construction of a reduced-order model such that the associated model error satisfies a prescribed H-infinity norm bound constraint. Two alternative methods for obtaining reduced-order models are presented. Sufficient conditions for the existence of desired reduced-order models are proposed in terms of linear matrix inequalities (LMIs) and a coupling non-convex rank constraint set. Conditions based on strict LMIs are obtained for the zeroth-order H-infinity approximation problem. When these conditions are satisfied, an explicit parametrization of the desired reduced-order models is also presented. All these results are extended to time-delay systems with parameter uncertainties. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed approach.