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You can constrain the gridded area (and hence the contours) to the area inside your data boundaries by either of these methods:

1. Use a fault file to define your data limits.
Create a BLN boundary file that defines the outline of your data limits and use the BLN file as a Fault file during gridding. In the Grid Data dialog box, click on the Advanced Options tab, go to the Breaklines and Faults tab, and specify the BLN as a fault file. Only some gridding methods support faults. Kriging does not, but Minimum Curvature (very similar to Kriging) does. For instructions on how to create a BLN file, please see: http://www.goldensoftware.com/activekb/questions/674

2. Blank outside the data limits.
Create a BLN boundary file defining the outline of your data limits and use Grid | Blank to blank the grid file outside the boundaries defined in the BLN file. For instructions on how to create a BLN file, please see: http://www.goldensoftware.com/activekb/questions/674

3. Use a different gridding method.
Use a different gridding method that doesn’t create data in areas where there were no data to begin with (ie. Triangulation or Natural Neighbor).

4. Grid the data and specify a reduced search radius.
Click on the Advanced Options button in the Grid Data dialog, then click on the Search tab. Remove the check mark from the No Search (use all of the data) if necessary, and specify the Radius 1 and Radius 2 values.

The default Kriging method offers the Search option. Other methods that offer it include Inverse Distance, Modified Shepard's Method, Nearest Neighbor, Radial Basis, Moving Average, Data Metrics, and Local Polynomial.

Some gridding methods do not have this option, including Minimum Curvature, Natural Neighbor, Polynomial Regression, and Triangulation.

Attached is an example file showig the results of methods 1-3.

See also: http://www.goldensoftware.com/activekb/questions/312