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Our goal is to determine, with high accuracy, the physical and orbitalparameters of two double-lined eclipsing binary systems, where the componentsare two giant stars. We also aim to study the evolutionary status of thebinaries, to derive the distances towards them by using a surfacebrightness-colour relation, and to compare these measurements with themeasurements presented by the Gaia mission. In order to measure the physicaland orbital parameters of the systems, we analysed the light curves andradial-velocity curves with the Wilson-Devinney code. We used V band and I-bandphotometry from the OGLE catalogue and near-infrared photometry obtained withthe New Technology Telescope (NTT) equipped with the SOFI instrument. Thespectroscopic data were collected with the HARPS spectrograph mounted at theESO 3.6m telescope and the MIKE spectrograph mounted at the 6.5m Claytelescope. We present the first analysis of this kind for two evolved eclipsingbinary systems from the OGLE catalogue: OGLE-BLG-ECL-305487 andOGLE-BLG-ECL-116218. The masses of the components of OGLE-BLG-ECL-305487 are$M_1$ = 1.059 $\pm$ 0.019 and $M_2$ = 0.991 $\pm$ 0.018 $M_\odot$, and theradii are $R_1$ = 19.27 $\pm$ 0.28 and $R_2$ = 29.99 $\pm$ 0.24 R$_\odot$. ForOGLE-BLG-ECL-116218, the masses are $M_1$= 0.969 $\pm$ 0.012 and $M_2$= 0.983$\pm$ 0.012 $M_\odot$, while the radii are $R_1$= 16.73 $\pm$ 0.28 and $R_2$=22.06 $\pm$ 0.26 $R_\odot$. The evolutionary status of the systems is discussedbased on the PARSEC and MIST isochrones. The ages of the systems wereestablished to be between 7.3-10.9 Gyr for OGLE-BLG-ECL-305487 and around 10Gyr for OGLE-BLG-ECL-116218. We also measured the distances to the binaries.For OGLE-BLG-ECL-305487, $d$= 7.80 $\pm$ 0.18 (stat.) $\pm$ 0.19 (syst.) kpcand for OGLE-BLG-ECL-116218, $d$= 7.57 $\pm$ 0.28 (stat.) $\pm$ 0.19 (syst.)kpc.

Evolved eclipsing binary systems in the Galactic bulge: Precise physical and orbital parameters of OGLE-BLG-ECL-305487 and OGLE-BLG-ECL-116218