Measuring the longest relaxation time of a viscoelastic liquid is an important step in its rheological characterization. In several instances, however, such measurement is unfeasible through conventional techniques, e.g., frequency response in linear viscoelasticity or measure of first normal stress difference. This difficulty is often found for very dilute macromolecular solutions. The case of polyelectrolyte solutions is especially important for their relevance in several bioengineering problems: Even theoretical predictions for this case can often not be tested in the absence of an experimental characterization. In this work, we succeed in measuring the relaxation time of two dilute/semidilute polyelectrolyte solutions as a function of added salt concentration. The relaxation time is measured through a novel microrheometrical technique based on the viscoelasticity-induced alignment of particles suspended in a microfluidic channel. We apply such technique to characterize two polyelectrolyte solutions, namely, hyaluronic acid and chitosan solutions. Relaxation times as small as approximate to 60 mu s are detected, which are otherwise unmeasurable when using both conventional or other mu-rheometrical techniques. (C) 2016 The Society of Rheology.