Élivágar is a novel, resource-efficient quantum circuit search (QCS) framework designed for Quantum Machine Learning (QML). It addresses the limitations of existing QCS methods by innovating in three key areas: search space, search algorithm, and candidate evaluation strategy. Traditional QCS methods often rely on classical Neural Architecture Search (NAS) techniques, which are not well-suited for quantum hardware due to differences in constraints such as noise and device topology. Élivágar introduces noise-guided and device topology-aware candidate generation, enabling hardware-efficient circuits and reducing the need for expensive circuit-mapping co-search. It also employs two cheap-to-compute predictors—Clifford noise resilience and representational capacity—to decouple noise robustness evaluation from performance, allowing early rejection of low-fidelity circuits and reducing evaluation costs. By using these predictors, Élivágar achieves higher accuracy and significantly faster performance compared to state-of-the-art QCS methods. Evaluations on 12 real quantum devices and 9 QML applications show that Élivágar achieves 5.3% higher accuracy and a 271× speedup. The framework is open-sourced for future research.Élivágar is a novel, resource-efficient quantum circuit search (QCS) framework designed for Quantum Machine Learning (QML). It addresses the limitations of existing QCS methods by innovating in three key areas: search space, search algorithm, and candidate evaluation strategy. Traditional QCS methods often rely on classical Neural Architecture Search (NAS) techniques, which are not well-suited for quantum hardware due to differences in constraints such as noise and device topology. Élivágar introduces noise-guided and device topology-aware candidate generation, enabling hardware-efficient circuits and reducing the need for expensive circuit-mapping co-search. It also employs two cheap-to-compute predictors—Clifford noise resilience and representational capacity—to decouple noise robustness evaluation from performance, allowing early rejection of low-fidelity circuits and reducing evaluation costs. By using these predictors, Élivágar achieves higher accuracy and significantly faster performance compared to state-of-the-art QCS methods. Evaluations on 12 real quantum devices and 9 QML applications show that Élivágar achieves 5.3% higher accuracy and a 271× speedup. The framework is open-sourced for future research.