Dense formate frameworks with a perovskite-like architecture exhibit multiferroic behavior and tunable mechanical properties. In such materials, interactions between the protonated amine and the metal-formate cavity have a large impact on the mechanical properties. We use complementary single-crystal X-ray diffraction and 1H solid state nuclear magnetic resonance spectroscopy to investigate amine-cavity interactions in [NH3NH2]Zn(HCOO)3. The results suggest that these interactions can be described as salt bridges similar to those in proteins and artificially synthesized helical polymers, where ionic interactions and hydrogen bonds are present at the same time. Nanoindentation and high-pressure single-crystal X-ray diffraction were used to study the mechanical properties of [NH3NH2]Zn(HCOO)3, yielding elastic moduli of E001 = 26.5 GPa and E110 = 24.6 GPa and a bulk modulus of K = 19 GPa. The mechanical properties suggest that, despite the relatively low packing density of [NH3NH2]Zn(HCOO)3, the amine-cavity interactions strengthen the framework significantly in comparison with related materials.