  The activity levels of the solar-twin candidates HD 101364 and HD 197027 are
measured and compared with the Sun, the known solar twin 18 Sco, and the
solar-like star 51 Peg. Furthermore, the absolute ages of these five objects
are estimated from their positions in the HR diagram and the evolutionary
(relative) age compared with their activity levels. To represent the activity
level of these stars, the Mount Wilson S-indices were used. To obtain
consistent ages and evolutionary advance on the main sequence, we used
evolutionary tracks calculated with the Cambridge Stellar Evolution Code. From
our spectroscopic observations of HD 101364 and HD 197027 and based on the
established calibration procedures, the respective Mount Wilson S-indices are
determined. We find that the chromospheric activity of both stars is comparable
with the present activity level of the Sun and that of 18 Sco, at least for the
period in consideration. Furthermore, the absolute age of HD 101364, HD 197027,
51 Peg, and 18 Sco are found to be 7.2, 7.1, 6.1, and 5.1 Gyr, respectively.
With the exception of 51 Peg, which has a significantly higher metallicity and
a mass higher by about 10% than the Sun, the present Sun and its twins compare
relatively well in their activity levels, even though the other twins are
somewhat older. Even though 51 Peg has a similar age of 6.1 Gyr, this star is
significantly less active. Only when we compare it on a relative age scale
(which is about 20% shorter for 51 Peg than for the Sun in absolute terms) and
use the higher-than-present long-term S$_{\rm{MWO}}$ average of 0.18 for the
Sun, does the S-index show a good correlation with evolutionary (relative) age.
This shows that in the search for a suitably similar solar twin, the relative
main-sequence age matters for obtaining a comparable activity level.
