Many people living with rare disease (RD) report a difficult diagnostic process from the symptom onset until they obtain the definitive diagnosis. The aim of this study was thus to ascertain the diagnostic process in RDs, and explore the determinants related with having to wait for more than one year in this process (defined as “diagnostic delay”). We conducted a case–control study, using a purpose-designed form from the Spanish Rare Diseases Patient Registry for data-collection purposes. A descriptive analysis was performed and multivariate backward logistic regression models fitted. Based on data on 1216 patients living with RDs, we identified a series of determinants associated with experiencing diagnostic delay. These included: having to travel to see a specialist other than that usually consulted in the patient’s home province (OR 2.1; 95%CI 1.6–2.9); visiting more than 10 specialists (OR 2.6; 95%CI 1.7–4.0); being diagnosed in a region other than that of the patient’s residence at the date of symptom onset (OR 2.3; 95%CI 1.5–3.6); suffering from a RD of the nervous system (OR 1.4; 95%CI 1.0–1.8). In terms of time taken to see a specialist, waiting more than 6 months to be referred from the first medical visit was the period of time which most contributed to diagnostic delay (PAR 30.2%). In conclusion, this is the first paper to use a collaborative study based on a nationwide registry to address the diagnostic process of patients living with RDs. While the evidence shows that the diagnostic process experienced by these persons is complex, more studies are needed to determine the implications that this has for their lives and those of their families at a social, educational, occupational, psychological, and financial level.