By using quantum Monte Carlo based stochastic analytic continuation(QMC-SAC)and spin wave theory,we study magnetic excitations of Heisenberg models with diagonally coupled checkerboard structures.We consider three kinds of checkerboard models(DC 2×2,DC 3×3,and CDC 3×3)consisting nearest-neighbor strong J1 and weak J2 antiferro-magnetic interactions.When the coupling ratio g=J2/J1 approaches 1,all three diagonal checkerboards have the same long-range antiferromagnetic Néel order at T=0.When g decreases,the quantum fluctuation can drive DC 2×2 model to quantum paramagnetic state,while DC 3×3 and CDC 3×3 models still have the long-range Néel order.By calculating the magnetic excitations at different coupling ratios,we find that the low-energy part of magnetic excitations calculated by QMC-SAC can be well explained by the spin wave theory.However,the high-energy parts even deep in the long-range an-tiferromagnetic phase are beyond the spin wave description.Compared to the g=1 uniform square lattice,the high-energy excitations are more rich in our models.Our study may also draw the attention to the high-energy exctitaions beyond the spin wave theory.