Microrheological measurements have been carried out on ionotropic gels made from an important cell wall polysaccharide, using diffusing wave spectroscopy and multiple particle tracking. These gels were formed by the interaction of calcium ions with negatively charged groups on the polymer backbone, which is a copolymer of charged and uncharged sugars, galacturonic acid, and its methylesterified analog, respectively. The results suggest that semiflexible networks are formed in these systems, with a low frequency, frequency independent storage modulus (G'>G''), and a high frequency scaling of both G' and G'' with omega3/4. The differences observed between gels obtained using polysaccharide samples with different amounts and patterns of the charged ion-binding groups could comfortably be accommodated within this theoretical framework, assuming that the elementary semiflexible elements of the network are filaments consisting of two polymer chains bridged with calcium. In particular, a sample that was engineered to possess a blockwise intramolecular distribution of calcium chelating moieties clearly exhibited the high frequency scaling of both moduli with omega3/4 across some three orders of magnitude, and the concentration dependences of the elastic modulus, at both high and low frequency, were found to follow power laws with predicted exponents. Furthermore, quantitative agreement of the moduli with theory was found for realistic estimates of the molecular parameters, suggesting that the physics of semiflexible networks is not only exploited by protein components of the cytoskeleton but also by polysaccharides in plant cell walls.