We report on a measurement of the ${B}_{d}^{0}$ mixing frequency and the calibration of an opposite-side flavor tagger in the D0 experiment. Various properties associated with the $b$ quark on the opposite side of the reconstructed $B$ meson are combined using a likelihood-ratio method into a single variable with enhanced tagging power. Its performance is tested with data, using a large sample of reconstructed semileptonic $B\ensuremath{\rightarrow}\ensuremath{\mu}{D}^{0}X$ and $B\ensuremath{\rightarrow}\ensuremath{\mu}{D}^{*}X$ decays, corresponding to an integrated luminosity of approximately $1\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$. The events are divided into groups depending on the value of the combined tagging variable, and an independent analysis is performed in each group. Combining the results of these analyses, the overall effective tagging power is found to be $\ensuremath{\epsilon}{\mathcal{D}}^{2}=(2.48\ifmmode\pm\else\textpm\fi{}{0.21}_{\ensuremath{-}0.06}^{+0.08})%$. The measured ${B}_{d}^{0}$ mixing frequency $\ensuremath{\Delta}{m}_{d}=0.506\ifmmode\pm\else\textpm\fi{}0.020(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.016(\mathrm{syst})\text{ }\text{ }{\mathrm{ps}}^{\ensuremath{-}1}$ is in good agreement with the world average value.