This paper deals with the problem of measuring the delay of a packet in a network with an associated error bound, but without having a need for clock synchronization and for any form of bidirectional messaging between the sender and receiver. A novel lightweight technique is proposed that aims at keeping the actual error made in the delay estimation very low while simultaneously providing a good error bound for each individual estimated packet delay. One-way delay measurement without clock synchronization and messaging cannot guarantee an error bound on delay estimations in general; however, we show that this is possible using periodic probe packets and appropriate assumptions that are compliant with the physical conditions of the environments within which the sender and receiver operate. Although we calculate an error bound for all our delay estimates, the main purpose is to have a much smaller actual error in these delay estimates in comparison with the computed error bound and other methods existing in the literature. The proposed method is evaluated against a recently reported technique of the same category and is shown to be much more superior overall.