  We report a comprehensive set of density functional theory calculations on
the family of layered antiferromagnetic manganese pnictides (Ba, Ca,
Sr)$\mathrm{Mn}_2\mathrm{(P, As, Sb)}_2$. We characterize all components to the
linear magnetoelectric (ME) tensor $\alpha$ which are parsed into their
contributions from spin and orbital moments for both lattice-mediated and their
clamped-ion electronic analogs. Our main results show that the orbital
magnetization components cannot be neglected in these systems. The ME response
is dominated by electronic effects with total $\alpha$ values exceeding those
of the prototypical $\mathrm{Cr}_2\mathrm{O}_3$ (i.e. $\alpha \simeq$ 6.79 ps/m
in $\mathrm{BaMn}_2\mathrm{As}_2$). We also identify a strong correlation with
the computed ME susceptibility on pnictogen substitution in the trigonal
subfamily albeit with weaker amplitudes ($\alpha \simeq$ 0.2-1.7 ps/m).
Additionally, we provide the dependence of these predictions on the Hubbard +U
correction, at the level of the local density approximation, which show large
variations on the calculated ME coefficients in the tetragonal compounds
highlighting the role of strong correlation in these compounds.
