We have been analyzing observed and simulated atmospheric motions to determine preferred small scale flow patterns and how those patterns are related to spatial scale and meteorological factors. These analyses and others that are planned to determine relationships between the patterns at different scales are most easily performed when vector components are available on a regular, three-dimensional grid, without any gaps or missing data. Unfortunately, the observations often have numerous missing values, and Large Eddy Simulations (LES) or Direct Numerical Simulations (DNS), while complete, are often calculated on variably-spaced grids. Thus, we have a need for a reliable interpolation method of predictable accuracy. Similar problems arise in nested grid models, and many areas of data analysis, so the results presented here have wide applicability. We have implemented several three-dimensional interpolation techniques. They include: (1) Inverse-distance weighting, (2) Simple linear interpolation, (3) Multiquadric interpolation (e. g., Nuss and Titley, 1994: Mon. Wea. Rev., 122, 1611-1631), (4) Least-squares linear regression with inverse distance weighting of observations, and (5) Least-squares polynomial (with two different polynomials) regression, also with inverse distance weighting of observations. We are testing these methods by randomly selecting points in LES vector fields for a stable flow over a wavy surface, and for convective, neutral, and stable boundary layers over a flat surface. We apply the interpolation schemes with data from nearby points to estimate the vector at the selected point. We then compare the original value with the estimate for each of the methods, and determine their performance. We are also conducting similar tests on sets of radar observations of atmospheric boundary layer motions. This paper reports the results of the comparisons, and of investigations of the effects of proximity of observations to the interpolation point