The reliable estimation of extreme quantiles is vital in various practical domains, among them economic policy development and financial risk assessment. Accurate quantile estimation is of key importance in computing risk measures such as Growth-at-Risk (GaR). This work explores the use of a conformal prediction-based methodology to obtain calibrated quantile estimates. We demonstrate the efficacy of this framework through extensive simulations and a detailed empirical study focused on GaR. Our findings reveal that conformal prediction improves the calibration accuracy and robustness of quantile estimations in extreme scenarios, where conventional approaches exhibit weaknesses. This advancement equips practitioners with robust analytical tools for evaluating and managing the likelihood of future extreme events.