The electromagnetic form factor provides important information on the internal structure of hadrons. Calculating these form factors pose significant challenges due to the unstable nature of most of the observed hadrons. In this work, we discuss the calculation of the form factors of the charged $\rho$-meson in a covariant formulation of the non-relativistic effective field theory, which has the advantage of splitting the contributions into a triangle diagram and a contact interaction diagram, the former of which has an ill-defined infinite volume limit. The couplings that parametrise the contact interaction diagram need to be fit to lattice data, for which we propose the background field method. This completes the framework necessary to extract the electromagnetic form factor of the charged $\rho$-meson from the lattice. Additionally, we also make use of $p^4$-order chiral perturbation theory to obtain crude estimates of the couplings in order to evaluate the form factors. The results show that the contact interactions have a substantial effect.