We propose to use longitudinal field muon-spin relaxation to investigate the excitation spectrum of the most successful realizations of one- and two-dimensional antiferromagnets from the coordination polymer materials. These are the one-dimensional system Cu(pyz)(NO3)2 and two-dimensional materials Cu(pyz)2(ClO4)2 and Cu(pyz)2(pyO)22. In each case we will measure the muon response to the excitation spectrum, identify diffusive behaviour and compare our results with those of other techniques.