This paper examines the absolute and relative robustness of two of the most common methods for estimating implied probability density functions (PDFs) – the double-lognormal approximating function and the smoothed implied volatility smile methods – using short sterling futures options and the FTSE 100 index options. The changes resulting from randomly perturbing quoted prices by no more than a half tick provide a lower bound on the confidence intervals of the summary statistics derived from the estimated PDFs. Our tests show that the smoothed implied volatility smile method dominates the double lognormal as a technique for estimating implied PDFs.