The seismic industry is increasingly acquiring broadband data in order to reap the benefits of extra low- and high-frequency contents. At the low end, as the sharp low-cut decay gets closer to zero frequency, it becomes harder for a well tie to estimate the low-frequency response correctly. The fundamental difficulty is that well logs are too short to allow accurate estimation of the long-period content of the data. Three distinctive techniques, namely parametric constant phase, frequency-domain least squares with multi-tapering, and Bayesian time domain with broadband priors, are introduced in this paper to provide a robust solution to the wavelet estimation problem for broadband seismic data. Each of these techniques has a different mathematical foundation that would enable one to explore a wide range of solutions that could be used on a case-by-case basis depending on the problem at hand. A case study from the North West Shelf Australia is used to analyse the performance of the proposed techniques. Cross-validation is proposed as a robust quality control measure for evaluating well-tie applications. It is observed that when the seismic data are carefully processed, then the constant phase approach would likely offer a good solution. The frequency-domain method does not assume a constant phase. This flexibility makes it prone to over-fitting when the phase is approximately constant. Broadband priors for the time-domain least-squares method are found to perform well in defining low-frequency side lobes to the wavelet.