(1) Background: As the number of people receiving specialized palliative care (PC) continues to rise, there is a need to ensure the transfer of this expertise from university-based PC departments to primary care hospitals without such in-house access. The present study examines the potential of telemedicine to bridge these gaps. (2) Methods: This is a prospective multi-center feasibility trial. All physicians were appropriately pre-equipped and instructed to conduct telemedical consultations (TCs), which took place within fixed meetings or on-call appointments either related or unrelated to individual patients (allowing TCs also for educational and knowledge exchange purposes). (3) Results: An inquiry for participation was submitted to 11 hospitals, with 5 external hospitals actively cooperating. In the first study section, a total of 57 patient cases were included within 95 patient-related TCs during 80 meetings. Other university disciplines were involved in 21 meetings (26.2%). Therapy adjustments resulted following 25 of 71 affected TCs (35.2%). In 20 cases (21.1%), an on-site consultation at the university hospital was avoided, and in 12 cases (12.6%), a transfer was avoided. Overall, TCs were considered helpful in resolving issues for 97.9% of the cases (n = 93). Yet, technical problems arose in about one-third of all meetings for at least one physician (36.2%; n = 29). Besides, in the second study section, we also conducted 43 meetings between physicians for education and knowledge exchange only. (4) Conclusions: Telemedicine has the potential to transfer university expertise to external hospitals through simple means. It improves collaboration among physicians, may prevent unnecessary transfers or outpatient presentations, and is thus likely to lower costs.