Background and Objectives: Rare diseases (RDs) are life-threatening or chronically impairing conditions that affect about 6% of the world’s population. RDs are often called ‘orphan’ diseases, since people suffering from them attract little support from national health systems. Aim: The aim of this study is to describe the clinical characteristics of, and the available laboratory examinations for, patients who were hospitalized in a tertiary referral center and finally received a diagnosis associated with a Rare Neurological Disease (RND). Materials and Methods: Patients that were hospitalized in our clinic from 1 January 2014 to 31 March 2022 and were finally diagnosed with an RND were consecutively included. The RND classification was performed according to the ORPHAcode system. Results: A total of 342 out of 11.850 (2.9%) adult patients admitted to our department during this period received a diagnosis associated with an RND. The most common diagnosis (N = 80, 23%) involved an RND presenting with dementia, followed by a motor neuron disease spectrum disorder (N = 64, 18.7%). Family history indicative of an RND was present in only 21 patients (6.1%). Fifty-five (16%) people had previously been misdiagnosed with another neurological condition. The mean time delay between disease onset and diagnosis was 4.24 ± 0.41 years. Conclusions: Our data indicate that a broad spectrum of RNDs may reach a tertiary Neurological Center after a significant delay. Moreover, our data underline the need for a network of reference centers, both at a national and international level, expected to support research on the diagnosis and treatment of RND.