You can display any linear grid with logarithmic contour levels by setting the Level method on the Levels page in the Properties window to Logarithmic. Depending on the Z range of the grid, that could give you a similar result to the Log, save as linear option with logarithmic contour levels, but not quite the same.
By gridding the data linearly, some of the extreme low and high values may have already been smoothed over. In addition, any negative or 0 values in the linear grid cannot be displayed with logarithmic contour levels and so extra steps should be taken to convert the negative or 0 data to a number >0.0.
Displaying a grid created with a linear scale as a contour map with logarithmic contours may be sufficient if you do not want to regrid the data or do not have the original data to regrid; but if you have logarithmically distributed data, it is most accurate to grid the log of the data.
Updated December 10, 2019