Mindfulness has received increasing interest in the scientific community due to its proved benefits within clinical settings and in increasing well-being. One challenge for mindfulness researchers is how to measure the construct without relying on self-report instruments, which are prone to biases. Here we tested two different computer-based tasks that aimed to get an objective measure of non-attachment (the Behavioral Attachment Task, BAT) and non-reactivity (the Non-Reactivity Assessment Task, NORAT). The BAT leverages the endowment effect, a concept from behavioral economics describing the attachment developed over time towards something we own, to measure increased reactions times to decisions to sell an object gifted to participants. We correlated changes in these reaction times after participants had owned these objects over a delay period with a Non-Attachment Scale commonly used in mindfulness studies using several versions of the test. However, the BAT failed to replicate the original endowment effect, and no significant correlations with mindfulness scores were found. The NORAT investigated the effect of non-task related emotional stimuli (Negative and Positive pictures) on response times to a two-alternative forced choice task, and correlated the degree of emotional interference with the non-reactivity subscale from the Five Facet Mindfulness Questionnaire. While negative pictures significantly increased reaction times, we did not find a correlation between this change and non-reactivity. In conclusion, the BAT and NORAT were not successful as objective measures of trait mindfulness, and further research is needed to explore novel ways of measuring these constructs.