High importance of the remote health monitoring (RHM) especially during and after the pandemic is accentuated in this article. It is displayed that by this way it is possible to revealing automatically situations "suspicious" from the COVID-19 illness view point for some concrete patients and also to keep up with possible complications after the illness. Another great opportunity of the RHM is connected with investigation of the vaccines. RHM allows reveal cases of the complications among the patients as well as positive and negative consequences of the vaccination. The general depersonalized data should be gathered and analyzed to research the regularities of the COVID-19 sickness rate and the complications frequency and also of the safety and effectiveness of the vaccines. It is proposed to combine advantages of RHM for medical care for concrete patients with opened opportunities for research to reveal important general normality connected with correlation between COVID-19 complications and peculiarities of various chronic diseases and specific medical statements. Telemedicine platform intended for creation of RHM systems is described. It has gone through the pilot running in Russian medical institutions and now presented good results have been achieved.