Hybrid organic-inorganic perovskites represent a special class of metal-organic framework where a molecular cation is encased in an anionic cage. The molecule-cage interaction influences phase stability, phase transformations, and the molecular dynamics. We examine the hydrogen bonding in four AmBX3 formate perovskites: [Am]Zn(HCOO)3, with Am+ = hydrazinium (NH2NH3+), guanidinium (C(NH2)3+), dimethylammonium (CH3)2NH2+, and azetidinium (CH2)3NH2+. We develop a scheme to quantify the strength of hydrogen bonding in these systems from first-principles, which separates the electrostatic interactions between the amine (Am+) and the BX3- cage. The hydrogen-bonding strengths of formate perovskites range from 0.36 to 1.40 eV/cation (8-32 kcalmol-1). Complementary solid-state nuclear magnetic resonance spectroscopy confirms that strong hydrogen bonding hinders cation mobility. Application of the procedure to hybrid lead halide perovskites (X = Cl, Br, I, Am+ = CH3NH3+, CH(NH2)2+) shows that these compounds have significantly weaker hydrogen-bonding energies of 0.09 to 0.27 eV/cation (2-6 kcalmol-1), correlating with lower order-disorder transition temperatures.