This paper aims to show how to improve the accuracy of formant frequency estimation in the singing voice of a lyric soprano. Conventional methods of formant frequency estimation may not accurately capture the formant frequencies of the singing voice, particularly in the highest pitch range of a lyric soprano, where the lowest formants are biased by the pitch harmonics. To address this issue, the study proposes adapting the Weighted Linear Prediction with Attenuated Main Excitation (WLP-AME) method for formant frequency estimation. Specific methods for glottal closure instant estimation were required due to differences in glottal closure patterns between speech and singing. The study evaluates the accuracy of the proposed method by comparing its performance with the LPC method through different pitch series arranged in an ascending musical scale. The results indicated that the adapted WLP-AME method consistently outperformed the LPC method in estimating formant frequencies of vowels sung by a lyric soprano. In addition, by estimating the formant frequencies of a synthetic /i/ vowel sung by a soprano singer at the musical note E5, the study showed that the adapted WLP-AME method provided formant frequency values closer to the correct values than those estimated by the LPC method. In general, these results suggest parameter values of AME function that optimize its performance, which can have applications in fields such as singing and medicine.