Stellar magnetic activity decays over the main-sequence life of cool stars due to the stellar spin-down driven by magnetic braking. The evolution of chromospheric emission is well studied for younger stars, but difficulties in determining the ages of older cool stars on the main sequence have complicated such studies for older stars in the past. Here, we report on chromospheric Ca II H and K line measurements for 26 main-sequence cool stars with asteroseismic ages older than a gigayear and spectral types F and G. We find that for the G stars and the cooler F-type stars that still have convective envelopes the magnetic activity continues to decrease at stellar ages above 1 Gyr. Our magnetic activity measurements do not show evidence for a stalling of the magnetic braking mechanism, which has been reported for stellar rotation versus age for G- and F-type stars. We also find that the measured R^' }_{ HK} indicator value for the cool F stars in our sample is lower than predicted by common age-activity relations that are mainly calibrated on data from young stellar clusters. We conclude that, within individual spectral type bins, chromospheric magnetic activity correlates well with stellar age even for old stars.