Decay spectroscopy of the odd-proton nuclei 249Md and 251Md has been performed. High-K isomeric states were identified for the first time in these two nuclei through the measurement of their electromagnetic decay. An isomeric state with a half-life of 2.8(5) ms and an excitation energy ≥910 keV was found in 249Md. In 251Md, an isomeric state with a half-life of 1.4(3) s and an excitation energy ≥844 keV was found. Similarly to the neighbouring 255Lr, these two isomeric states are interpreted as 3 quasi-particle high-K states and compared to new theoretical calculations. Excited nuclear configurations were calculated within two scenarios: via blocking nuclear states located in proximity to the Fermi surface or/and using the quasiparticle Bardeen–Cooper–Schrieffer method. Relevant states were selected on the basis of the microscopic-macroscopic model with a deformed Woods–Saxon potential. The most probable candidates for the configurations of K-isomeric states in Md nuclei are proposed.