Parameter estimation of the 2R-1C model is usually performed using iterative methods that require high-performance processing units. Consequently, there is a strong motivation to develop less time-consuming and more power-efficient parameter estimation methods. Such low-complexity algorithms would be suitable for implementation in portable microcontroller-based devices. In this study, we propose the quadratic interpolation non-iterative parameter estimation (QINIPE) method, based on quadratic interpolation of the imaginary part of the measured impedance, which enables more accurate estimation of the characteristic frequency. The 2R-1C model parameters are subsequently calculated from the real and imaginary parts of the measured impedance using a set of closed-form expressions. Comparative analysis conducted on the impedance data of the 2R-1C model obtained in both simulation and measurements shows that the proposed QINIPE method reduces the number of required measurement points by 80% in comparison with our previously reported non-iterative parameter estimation (NIPE) method, while keeping the relative estimation error to less than 1% for all estimated parameters. Both non-iterative methods are implemented on a microcontroller-based device; the estimation accuracy, RAM, flash memory usage, and execution time are monitored. Experiments show that the QINIPE method slightly increases the execution time by 0.576 ms (about 6.7%), and requires 24% (1.2 KB) more flash memory and just 2.4% (32 bytes) more RAM in comparison to the NIPE method. However, the impedance root mean square errors (RMSEs) of the QINIPE method are decreased to 42.8% (for the real part) and 64.5% (for the imaginary part) of the corresponding RMSEs obtained using the NIPE method. Moreover, we compared the QINIPE and the complex nonlinear least squares (CNLS) estimation of the 2R-1C model parameters. The results obtained show that although the estimation accuracy of the QINIPE is somewhat lower than the estimation accuracy of the CNLS, it is still satisfactory for many practical purposes and its execution time reduces to 145−1 30.