We present the first modern analysis of two young, eclipsing binaries, EK Cep and HS Her, based on new, ground-based, CCD multicolour light curves as well as the TESS observations, radial velocity curves, and eclipse timing measurements. The orbital and stellar parameters of the stars are determined by Roche modelling, and their evolutionary status is examined using a grid of isochrones and evolutionary tracks. We find that HS Her is 25-32 Myr old and its components are on the zero-age main sequence; at the age of 16-20 Myr, the primary of EK Cep is also on the ZAMS, but its secondary is a pre-main-sequence star. Both binaries have slightly eccentric orbits and display apsidal motion. Based on updated eclipse timings and spectroscopic evidence, we rule out the presence of a previously hypothesized tertiary component in HS Her.