AbstractStrong magnetic coupling between the spins of unpaired electrons is an essential ingredient of many fascinating physical phenomena. Here we report calculations using the hybrid HSE06 functional of magnetic superexchange constants, J, for a series of low‐dimensional CuII and AgII binary and ternary systems with fluoride and oxide ligands. The calculations correctly reproduce the sign and size of the magnetic superexchange constants for prototypical antiferromagnetic (AFM) 1D (J1D) and 2D (J2D) systems, while overestimating the absolute values of J by about 11 %. We find that [AgF][BF4], a quasi‐1D system with linear infinite [AgIIF+] chains, is predicted to exhibit an unprecedented strong AFM superexchange via one atom (F), with J1D about −300 meV. Compression of [AgF][BF4] to 10 GPa should lead to a further increase in AFM interactions with J1D reaching −360 meV at 10 GPa.