Quantum dots and antidots made of two-dimensional materials are often used to design novel nanoscale devices due to their peculiar physical properties. For example, silicene manifests a remarkable intrinsic spin-orbit interaction that triggers a topological phase transition in the low-energy regime. We found that the protected edge states present in silicene antidots and dots are polarized in valley-spin pairs. Our calculations also confirmed that the topological edge states are propagating over the perimeter of the antidot/dot for both ideal or realistic edge termination containing roughness on the atomic length scale. Here we also propose an experimental method for the detection of bound states around an antidot formed from a hole in a graphene sheet by measuring the ballistic two terminal conductances. In particular, we consider the effect of bound states formed by magnetic field on the two terminal conductance and show that one can observe Breit-Wigner like resonances in the conductance as a function of the Fermi level close to the energies of the bound states.