We study the radiative transitions between vector and pseudoscalar quarkonia in the light-front Hamiltonian approach, and investigate the effects of using different current component and different reference frames. In practical calculations with truncated Fock spaces, transition form factors may acquire current component dependence and frame dependence, and such dependences could serve as a measure for the Lorentz symmetry violation. We suggest using the transverse current with $m_j=0$ state of the vector meson, since this procedure employs the dominant spin components of the light-front wavefunctions and is more robust in practical calculations. We calculate the transition form factor between vector and pseudoscalar quarkonia and investigate the frame dependence with light-front wavefunctions calculated from the valence Fock sector. We suggest using frames with minimal longitudinal momentum transfer for calculations in the valence Fock sector, namely the Drell-Yan frame for the space-like region and a specific longitudinal frame for the timelike region; at $q^2=0$ these two frames give the same result.