We present state-of-the-art predictions for $t\bar{t}\gamma$ and $t\bar{t}Z(Z \to \nu_\ell\bar{\nu}_\ell)$ production in the fully leptonic channel at the LHC. The first process can provide key information on the strength and structure of the top-quark coupling to the photon. The invisible-decay channel $t\bar{t}Z(Z \to \nu_\ell\bar{\nu}_\ell)$ is an important SM background for Dark Matter searches in $t\bar{t}+E_{T}^{miss}$ final states. Our results are accurate to NLO in QCD and include all resonant and non-resonant diagrams, interferences and off-shell effects for top quarks and $W/Z$ bosons. As such, they represent the most complete description of these processes from the viewpoint of a fixed-order calculation. We show selected results for the LHC Run II energy of 13 TeV, focusing on the impact of choosing well motivated scales and on the effect of using different approaches for the modeling of top quark decays.