(1) Background: The Milan System for Reporting Salivary Gland Cytopathology (MSRSGC) was introduced in 2018, bringing an organ-specific classification system for salivary gland cytopathology. The aim of present study is to evaluate the MSRSGC prospectively, based on a two-year experience in the tertiary care center pathology department, and evaluate the role of routine cell block (CB) preparation in salivary gland cytopathological diagnostics. (2) Methods: In our institution, the Department of Pathology, Fimlab Laboratories, Tampere, Finland, the MSRSGC has been implemented in salivary gland cytopathology since January 2018 and, over a two-year period (January 2018–December 2019), there were 365 fine-needle aspirations, of which 164 had a surgical follow-up. The CB methods used were Plasma-thrombin, the collection of visible fragments, and the Shandon and in-house methods. (3) Results: The MSRSGC diagnostic figures were as follows: accuracy 87.5%, sensitivity 45.8% and specificity 98.9%. For diagnostic categories of MSRSGC (non-neoplastic, benign neoplasm and malignant neoplasm) (n = 63) diagnostic accuracy was 98.4%, and for undetermined categories (atypia of undetermined significance, salivary gland neoplasm of uncertain malignant potential and suspicious for malignancy) (n = 49) diagnostic accuracy was 73.5%. Non-contributory cell blocks resulted more often in a false negative diagnosis (25%, 3/12) than a true negative diagnosis (10%, 7/73, p < 0.001), and is, most likely, an insufficient cytological diagnosis (86%, 18/21, p < 0.001). (4) Conclusion: The application of MSRSGC and CBs are beneficial in salivary gland cytological diagnosis, increasing diagnostic accuracy and, thus, patients’ management and treatment.