Although it is possible to hack the properties of contour to change where the z values appear, it is typically much easier to create a hgtransform() group, and when you contour() use that group's handle as the first parameter to contour() (the position you would specify the axes). Then set the transform matrix of the hgtransform group to translate Z upwards by however many units are appropriate. If you use datatips, then they will reflect the original data values, not the translated values.
The code suggested by Jacob Wood does work for its purpose, and can be used with contour() as well as contourf(), but it relies upon subtracting enough from the Z coordinates that all of the Z coordinates passed to surf() are negative. Then you either have to live with the z axes be offset by that subtracted amount, or else you have to set the Z tick labels to hide the fact that your data is offset. Your ability to use datatips is affected when you use this approach.