1. Use a different gridding method.
The default Kriging method creates trends in your data and can extrapolate the Z values in the grid file to extend past the limits of the Z data in your original file. Some gridding methods do not extrapolate the Z range in the grid beyond the range of the data. These methods include: Inverse Distance to a Power, Natural Neighbor, Nearest Neighbor, and Trinagulation with Linear Interpolation. If you are getting negative Z values in the grids produced with these gridding methods, please check the original data file to be sure there are no negative values.

2. Use Grid Math to eliminate the negative values.
Another method to remove negative data is to simply convert them to 0. Go to Grid | Math, select your existing grid file and click Open. In the Grid Math dialog box, this grid is Input Grid File (A). Specify a new name for the Output Grid File (C), and enter the formula C = max(A,0). This formula converts all negative Z values to 0 in the new grid file. Click OK and the new grid file is created.

3. Transform your original Z values to logarithmic values.
If your data range over several orders of magnitude, it may be beneficial to transform your Z values in the worksheet to logarithmic values. Open the data file in the worksheet and choose Data| Transform. If your data are in column C, and column D is blank, use the formula D = log10(C) to calculate the log base 10 of the Z values. Save the worksheet, and create a grid using column D as the source of Z values. This method may create negative log10 values, but these values represent small positive Z values. e.g. log10(Z) = -2, then Z = 0.01.