Salivary alpha-amylase (sAA) is an enzyme found in saliva and is considered a noninvasive biomarker for sympathetic nervous system activity. While a wide range of sAA activity in response to stress has been reported in nonhuman primates, the effects of stress on sAA activity in common marmosets are still unknown. We tested the hypothesis that advanced age and cognitive function may have an impact on stress-related sAA reactivity in marmosets. Thirteen marmosets (nine males and five females) had saliva samples collected during a stressful condition (manual restraint stress) at two different time points, with a 60-min interval. On the next day, the animals underwent the object recognition test (ORT, a type of cognitive test), and then oral examinations. The animals were categorized into two age groups: old (10-13 years), and very old (15-22 years). Irrespective of age, sAA levels showed a significant difference between T1 (mean 2.07 ± 0.86 U/mL) and T2 samples (mean 1.03 ± 0.67 U/mL), with higher values observed at T1 (p < 0.001). The intra-assay coefficients of variation (CV) for low and high sAA concentrations were 10.79% and 8.17%, respectively, while the interassay CVs for low and high sAA concentrations were 6.39% and 4.38%, respectively. Oral health issues were common but did not significantly impact sAA levels. The ORT indicated that the animals could recognize an object placed in the cage 6 h after familiarization. In conclusion, all marmosets showed a higher sAA concentration in the first saliva sample as compared to the second saliva sample collected 1 h later, indicating adaptation to stress. No significant differences in sAA levels were observed between sexes, ORT performance, or oral health. Our results indicate that autonomic responsivity and cognitive (memory) functions were preserved even in very old marmosets.