  Decay spectroscopy of the odd-proton nuclei $^{249}$Md and $^{251}$Md 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 $\geq
910$ keV was found in $^{249}$Md. In $^{251}$Md, an isomeric state with a
half-life of $1.4(3)$ s and an excitation energy $\geq 844$ keV was found.
Similarly to the neighbouring $^{255}$Lr, 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.
