Biometric data are sensitive according to personal data regulations and ISO/IEC 24745. In a biometric recognition system, biometric data should be protected from their generation to their comparison. In this work, we combine postquantum homomorphic encryption using CRYSTALS-Kyber (the base post-quantum algorithm of the FIPS 203 standard for module-lattice-based key-encapsulation mechanism, recently approved by the NIST) with Garbled Circuits, which allow different parties to compute the result of an operation from private inputs. We propose a protected biometric authentication scheme in which homomorphic encryption with CRYSTALS-Kyber public-key encryption computes the difference between the reference and a query, and a Garbled Circuit (GC) performs the comparison with a threshold. Two GC frameworks, TinyGarble (based on Verilog) and TinyGarble2 (based on C++), are employed to design a privacy-preserving face authentication system with FaceNet embeddings. The two frameworks are compared in terms of design and computation costs. In any case, the authentication takes, approximately, 0.5 seconds.