Magnetospheric magnetic field models are crucial for many space weather applications. However, the latest empirical models require solar wind and IMF data, which are not always available. Data gaps are especially common for times before the launch of the WIND spacecraft at the end of 1994, but even after then there are data gaps. We present a method to interpolate the solar wind characteristics across data gaps and to evaluate the W parameters needed for the TS05 model (Tsyganenko and Sitnov, 2005). Within some distance from the edge of a data gap, the solar wind parameters from our method yield a better estimate of the observed magnetic field than that which could be found using average values of the parameters. Deep within data gaps (far from measured values), the interpolated parameters are reasonable, or typical values, no better or worse than average values. We have created a database of hourly data with solar wind characteristics, G, and W parameters from 1963 to 31 May 2007, which is sufficient for use in all the Tsyganenko models, including the latest TS05 model. Our comparisons of the model and observed magnetic field at geosynchronous orbit give an estimate of the error in the model field as a function of status parameters defined by the interpolation scheme. We also show that the model field is on average just as accurate using the hourly data as that based on 5 min data (at least at geosynchronous orbit).