Abstract The electroencephalogram (EEG) is one of the main tools for non-invasively studying brain function and dysfunction. To better interpret EEGs in terms of neural mechanisms, it is important to compare experimentally recorded EEGs with the output of neural network models. Most current neural network models use networks of simple point neurons. They capture important properties of cortical dynamics, and are numerically or analytically tractable. However, point neuron networks cannot directly generate an EEG, since EEGs are generated by spatially separated transmembrane currents. Here, we explored how to compute an accurate approximation of the EEG with a combination of quantities defined in point-neuron network models. We constructed several different candidate approximations (or proxies) of the EEG that can be computed from networks of leaky integrate-and-fire (LIF) point neurons, such as firing rates, membrane potentials, and specific combinations of synaptic currents. We then evaluated how well each proxy reconstructed a realistic ground-truth EEG obtained when the synaptic input currents of the LIF network were fed into a three-dimensional (3D) network model of multi-compartmental neurons with realistic cell morphologies. We found that a new class of proxies, based on an optimized linear combination of time-shifted AMPA and GABA currents, provided the most accurate estimate of the EEG over a wide range of network states of the LIF point-neuron network. The new linear proxies explained most of the variance (85-95%) of the ground-truth EEG for a wide range of cell morphologies, distributions of presynaptic inputs, and position of the recording electrode. Non-linear proxies, obtained using a convolutional neural network (CNN) to predict the EEG from synaptic currents, increased proxy performance by a further 2-8%. Our proxies can be used to easily calculate a biologically realistic EEG signal directly from point-neuron simulations and thereby allow a quantitative comparison between computational models and experimental EEG recordings. Author summary Networks of point neurons are widely used to model neural dynamics. Their output, however, cannot be directly compared to the electroencephalogram (EEG), which is one of the most used tools to non-invasively measure brain activity. To allow a direct integration between neural network theory and empirical EEG data, here we derived a new mathematical expression, termed EEG proxy, which estimates with high accuracy the EEG based simply on the variables available from simulations of point-neuron network models. To compare and validate these EEG proxies, we computed a realistic ground-truth EEG produced by a network of simulated neurons with realistic 3D morphologies that receive the same spikes of the simpler network of point neurons. The new obtained EEG proxies outperformed previous approaches and worked well under a wide range of simulated configurations of cell morphologies, distribution of presynaptic inputs, and position of the recording electrode. The new proxies approximated well both EEG spectra and EEG evoked potentials. Our work provides important mathematical tools that allow a better interpretation of experimentally measured EEGs in terms of neural models of brain function.