A direct ${Q}_{\mathrm{EC}}$-value measurement of the superallowed ${\ensuremath{\beta}}^{+}$ emitter $^{22}\mathrm{Mg}$ was performed using TRIUMF's Ion Trap for Atomic and Nuclear Science. The direct ground-state to ground-state atomic mass difference between $^{22}\mathrm{Mg}$ and $^{22}\mathrm{Na}$ was determined to be ${Q}_{\mathrm{EC}}=4781.40(22)$ keV, representing the most precise single measurement of this quantity to date. In a continued push toward calculating superallowed isospin-symmetry-breaking corrections from first principles, ab initio shell-model calculations of the $A=22$ isobaric multiplet mass equation are also presented for the first time using the valence-space in-medium similarity renormalization group formalism. With particular starting two- and three-nucleon forces, this approach demonstrates good agreement with the experimental data.