Counterfeit devices are a growing threat to trust in electronic devices, involving the production and distribution of fake components or reselling out-of-spec ones. These pose risks like compromised functionality, security vulnerabilities, and economic losses when purchasing Commercial Off-The-Shelf (COTS) devices like FPGA and microcontrollers. To address this, we introduce VARI-CHECK, a low-overhead method for authenticating COTS devices. VARI-CHECK leverages inherent fabrication process variations to create digital signatures for device authentication. We validate this approach through experiments on FPGA devices, training a machine learning model to identify non-original devices. We test it on 100 oscillating/bistable circuit elements across 40 FPGA devices, achieving 80.4% success with Isolation Forest and 81.25% with One Class SVM.