Olfactory dysfunction associated with coronavirus 2 (SARS-CoV-2) infection is in most cases transient, recovering spontaneously within a few days. However, in some patients it persists for a long time, affects their everyday life and endangers their health. Hence, we focused on patients with persistent loss of smell. The aim of this study was to evaluate olfactory dysfunction using a standardized test. Due to the pandemic, olfactory testing was performed online. Smell tests (Odorized Markers Test, OMT) were sent home to the patients. Together with the smell self-testing, participants reported and assessed several parameters (age, sex, subjective assessment of smell and taste, nasal patency, etc.) in an online questionnaire. Based on the questionnaire outcomes, the results were sent to the patients along with a list of participating otolaryngologists who provided them with professional care. From March to June 2021, 1025 patients requested smell testing, of these, 824 met the inclusion criteria of this study. The duration of the olfactory dysfunction at the time of testing ranged from 1 month to 1 year. Using the OMT, impaired smell ability—anosmia or hyposmia—was confirmed in 82.6% of participants. A total of 17.4% of participants were determined to be normosmic however, more than 50% of them complained of parosmia and/or phantosmia. Our study demonstrates the relevance of psychophysical smell testing and its suitability for remote use during the pandemic. This study also revealed several correlations between prolonged olfactory dysfunction and the monitored parameters.