Override class method in unit test to return expected results

In a unit test, I would like to be able to change the default behaviour of a method for a class instance in order to validate that my class handles the edge case properly.

For example,

In my test case when I make a call as follows

System.Data.SqlClient.SqlConnection conn = new System.Data.SqlClient.SqlConnection ();

For this particular test case I want it to always return an Exception with particular details.

This way I can always ensure that the code for database connection failures work.

Any thoughts on how I might solve this problem.