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.
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