Temperature-dependent electron paramagnetic resonance studies of charge-ordered<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Nd</mml:mi></mml:mrow><mml:mrow><mml:mn>0.5</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow><mml:mrow><mml:mn>0.5</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal…

We report electron paramagnetic resonance measurements on single crystalline and powder samples of ${\mathrm{Nd}}_{0.5}{\mathrm{Ca}}_{0.5}{\mathrm{MnO}}_{3}$ across the charge-ordering transition at ${T}_{\mathrm{co}}=240\mathrm{K}$ down to the antiferromagnetic ordering transition at ${T}_{N}=140\mathrm{K}.$ The changes in the linewidth, g-factor and intensity as functions of temperature are studied to understand the nature of spin-dynamics in the system. We explain the observed large decrease in the linewidth from ${T}_{N}$ to ${T}_{\mathrm{co}}$ in terms of motional narrowing caused by the hopping of the Jahn--Teller polarons yielding an activation energy of ${E}_{a}=0.1\mathrm{}\mathrm{eV}.$ Similar analysis of data on ${\mathrm{Pr}}_{0.6}{\mathrm{Ca}}_{0.4}{\mathrm{MnO}}_{3}$ published earlier gives ${E}_{a}=0.2\mathrm{eV}.$ Below ${T}_{\mathrm{co}},$ the g-value increases continuously suggesting a gradual strengthening of the orbital ordering. We give a qualitative explanation of the maximum in the asymmetry ratio A/B observed at ${T}_{\mathrm{co}}$ and its temperature dependence in single crystal spectra which also supports the model of motional narrowing.