The broad-bandwidth capabilities of next generation telescopes such as the JVLA mean that the spectrum of any given source varies significantly within the bandwidth of any given observation. Detailed spectral analysis taking this variation into account is set to become standard practice when dealing with any new broadband radio observations; it is therefore vital that methods are developed to handle this new type of data. In this paper, we present the Broadband Radio Astronomy ToolS (BRATS) software package and, use it to carry out detailed analysis of JVLA observations of three powerful radio galaxies. We compare two of the most widely used models of spectral ageing, the Kardashev-Pacholczyk and Jaffe-Perola models and also results of the more complex, but potentially more realistic, Tribble model. We find that the Tribble model provides both a good fit to observations as well as providing a physically realistic description of the source. We present the first high-resolution spectral maps of our sources and find that the best-fitting injection indices across all models take higher values than has previously been assumed. We present characteristic hot spot advance speeds and make comparison to those derived from dynamical ages, confirming the previously known discrepancy in speed remains present when determined at high spectral resolutions. We show that some previously common assumptions made in determining spectral ages with narrow-band radio telescopes may not always hold and strongly suggest these are accounted for in future investigations. ; Comment: 24 Pages, 13 Figures, 7 Tables, Accepted by MNRAS