The problem of H-infinity filtering for continuous-time linear systems with time-delayed measurement is investigated. The authors develop a methodology for designing linear filters which ensure a prescribed bound on the L-2 induced gain from the noise signals to the estimation error. Filtering problems for time-varying systems over a finite-horizon, as well as stationary infinite-horizon filtering for time-invariant systems, are tackled. In the finite horizon case, our estimation procedure entails an overdesign that stems from the last d seconds of the time interval [0. T], where d is the delay length. This overdesign becomes smaller as T increases, and it vanishes in the infinite-horizon case.