We correlate conformation and dynamics of the semirigid polyelectrolytes deoxyribonucleic acid (DNA) and hyaluronic acid (HA) in the semidilute regime, across a broad concentration range (10(-3) - 10(2) g/L). Salt-free polyelectrolytes are distinct from uncharged polymers as they presumably form a rather rigid, isotropic mesh. The polyelectrolyte characteristic mesh size is known as de Gennes correlation length xi. We directly probed the mesh formed by DNA and HA, by employing fluorescence correlation spectroscopy (FCS) to measure the diffusion coefficient of fluorescently labeled DNA fragments added in trace amounts. For the salt-free solutions we found that the DNA or HA mesh size has to be 2-3 times larger than the fragments for them to start to diffuse freely (as if in the dilute solution). For a tighter mesh (concentrations 0.1-1 g/L), the fragment diffusion coefficient is only half the free diffusion value. Conversely, fragments show the free diffusion coefficient-as if there is no mesh-in DNA or HA in 10 mM buffer. This complies well with the fact that the xi fades for polyelectrolytes with added salt. The diffusion coefficient falls off further when the mesh size gets smaller than the fragment size (above 1 g/L) and a similar value is reached in buffer as well as in pure water, respectively, at the highest measured concentrations (10 g/L). We also performed small-angle X-ray scattering (SAXS) on HA and DNA (range 3-130 g/L) to complement our previous dielectric spectroscopy (DS) studies (range 0.01-5 g/L). Combined, these methods provide reference values of the de Gennes length xi across the range studied by FCS.