We review examples of muon-spin relaxation measurements on molecule-based magnetic coordination polymers, classified by their magnetic dimensionality. These include the one-dimensional s=1/2 spin chain Cu(pyz)(NO3)2 and the two-dimensional s=1/2 layered material [Cu(HF2)(pyz)2]BF4. We also describe some of the more exotic ground states that may become accessible in the future given the ability to tune the interaction strengths of our materials through crystal engineering.