Background: Herpesviruses cause a variety of infections, ranging from localized inflammation to severe disease and malignancies. The current portfolio of anti-herpes drugs is limited, often accompanied by significant side effects, and prolonged use can lead to viral resistance. This study investigates the antiviral activity of newly synthesized compounds against cytomegalovirus (CMV) and herpes simplex virus (HSV). Methods: Saturated heterocyclic compounds with annelated or spiro rings have been synthesized using either the aza-Cope–Mannich rearrangement or the alkene metathesis reaction as the key step of the transformation. Cytotoxicity was assessed using the MTT assay, while antiviral activity was measured by changes in viral titer in the presence of the compounds. Results: Several promising lead compounds were identified. A time-of-addition assay indicated that the primary targets are likely viral DNA polymerase, with inhibition leading to a halt in viral protein synthesis. Conclusions: We identified two active compounds that inhibit both herpesviruses, likely targeting the viral replicative complex.