Introduction: Rare disease referral centres are entrusted with missions of clinical expertise and research, two activities that have to contend with numerous obstacles. Providing specialist opinions is time-consuming, uncompensated and limited by difficulties in exchanging medical data. Clinical research is constrained by the need for frequent research protocol visits. Our objective was to determine whether telemedicine (TLM) can overcome these difficulties. Methods: To better characterise the activity of clinical expertise provided by our French centre, each opinion delivered by our team was reported on a standardised form. To investigate our clinical research activity, investigators and patients were asked to complete a questionnaire on the acceptability of research protocol teleconsultations. Results: Regarding clinical expertise, our team delivered 120 opinions per week (representing a total of 21 h), of which 29% were delivered to patients and 69% to medical practitioners. If these were delivered using TLM, it would represent a potential weekly income of EUR 500 (tele-expertise) and EUR 775 (teleconsultations). Regarding the research activity, 70% of investigators considered the frequency of visits to be a limiting factor for patient inclusions; nearly half of the patients surveyed would be in favour of having teleconsultations in place of (40%) or in addition to (56%) in-person visits. Conclusion: Whereas TLM has become widely used as a back-up procedure to in-person consultations during the COVID-19 pandemic, the solutions it provides to the problems encountered in performing expertise and research activities have made it a new conventional follow-up modality for patients with rare diseases.