One of the most common measurement artifacts present in Electrical Bioimpedance Spectroscopy measurements (EBIS) comes from the capacitive leakage effect resulting from parasitic stray capacitances. This artifact produces a deviation in the measured impedance spectrum that is most noticeable at higher frequencies. The artifact taints the spectroscopy measurement increasing the difficulty of producing reliable EBIS measurements at high frequencies. In this work, an approach for removing such capacitive influence from the spectral measurement is presented making use of a novel method to estimate the value of the parasitic capacitance equivalent that causes the measurement artifact. The proposed method has been tested and validated theoretically and experimentally and it gives a more accurate estimation of the value of the parasitic capacitance than the previous methods. Once a reliable value of parasitic capacitance has been estimated the capacitive influence can be easily compensated in the EBIS measured data. Thus enabling analysis of EBIS data at higher frequencies, i.e. in the range of 300-500 kHz like measurements intended for cerebral monitoring, where the characteristic frequency is remarkably higher than EBIS measurements i.e. within the range 30 to 50 kHz, intended for body composition assessment.