Mass-loss of red giant branch (RGB) stars is still poorly determined, despite its crucial role in the chemical enrichment of galaxies. Thanks to the recent detection of solar-like oscillations in G–K giants in open clusters with Kepler, we can now directly determine stellar masses for a statistically significant sample of stars in the old open clusters NGC 6791 and 6819. The aim of this work is to constrain the integrated RGB mass-loss by comparing the average mass of stars in the red clump (RC) with that of stars in the low-luminosity portion of the RGB [i.e. stars with L≲L(RC)]. Stellar masses were determined by combining the available seismic parameters νmax and Δν with additional photometric constraints and with independent distance estimates. We measured the masses of 40 stars on the RGB and 19 in the RC of the old metal-rich cluster NGC 6791. We find that the difference between the average mass of RGB and RC stars is small, but significant [ (random) ±0.04 (systematic) M⊙]. Interestingly, such a small does not support scenarios of an extreme mass-loss for this metal-rich cluster. If we describe the mass-loss rate with Reimers prescription, a first comparison with isochrones suggests that the observed is compatible with a mass-loss efficiency parameter in the range 0.1 ≲η≲ 0.3. Less stringent constraints on the RGB mass-loss rate are set by the analysis of the ∼2 Gyr old NGC 6819, largely due to the lower mass-loss expected for this cluster, and to the lack of an independent and accurate distance determination. In the near future, additional constraints from frequencies of individual pulsation modes and spectroscopic effective temperatures will allow further stringent tests of the Δν and νmax scaling relations, which provide a novel, and potentially very accurate, means of determining stellar radii and masses.