The REBCO high-temperature superconducting tape has a pronounced electromagnetic anisotropy. The critical current is strongly dependent on the value of the magnetic field, the magnetic field direction, the temperature, and the stress, and has a significant nonlinear relationship. It is also important to note that screening current effects in superconducting magnets at elevated temperatures lead to a non-uniform distribution of current densities, and thus the inductance of superconducting magnets at high-temperatures is calculated differently from that of normal magnets. This is essential for the design of superconducting energy storage magnets at high-temperatures, especially for the accurate evaluation of the inductance values. To further analyze the variation of the inductance value due to the REBCO screening current, the T-A formulation combined with the magnetic energy density is considered to evaluate the energy storage and inductance values during the excitation of the superconducting coil. The effect of excitation rate, operating temperature, and excitation current on the inductance value is analyzed based on the design of a 5T insulating superconducting coil. The mathematical relation between excitation voltage, contact resistance, and inductance in the magnetic excitation experiment is presented, and the accuracy of the calculated method is verified by comparison with simulation results.