Nuclear magnetic quadrupole moments (MQMs), such as intrinsic electric dipole moments of elementary particles, violate both parity and time-reversal symmetry and, therefore, probe physics beyond the standard model. We report on accurate relativistic coupled cluster calculations of the nuclear MQM interaction constants in BaF, YbF, BaOH, and YbOH. We elaborate on estimates of the uncertainty of our results. The implications of experiments searching for nonzero nuclear MQMs are discussed.