A new dual-log spiral geometry is proposed for microstrip resonators, offering substantial advantages in performance and size reduction at subgigahertz frequencies when realized in superconducting materials. The spiral is logarithmic in line spacing and width such that the width of the spiral line increases smoothly with the increase of the current density, reaching its maximum where the current density is maximum (in its center for λ/2 resonators). Preliminary results of such a logarithmic ten-turn (2 × 5 turns) spiral, realized with double-sided YBCO thin film, showed a Q.-factor seven times higher than that of a single ten-turn uniform spiral made of YBCO thin film and 64 times higher than a copper counterpart. The insertion loss of the YBCO dual log-spiral has a high degree of independence of the input power in comparison with a uniform Archimedian spiral, increasing by only 2.5% for a 30-dBm increase of the input power, compared with nearly 31% for the uniform spiral. A simple approximate method, developed for prediction of the resonant frequency of the new resonators, shows a good agreement with the test results.