I have a private static readonly field in my class:
public class MyClass
{
    // ISSUE #1 -- requires unproven: path != null
    private static readonly DirectoryInfo MyDirectory =
        new DirectoryInfo(Settings.Default.MyDirectoryPath);
    protected virtual void SomeMethod()
    {
        if (MyDirectory.Exists)
        {
            // ISSUE #2 -- requires unproven: !string.IsNullOrEmpty(path)
            var catalog = new DirectoryCatalog(MyDirectory.FullName);
        }
    }
}
For issue #1 I used a null coalescing operator to default to some magic string and that fixed it, but I don't really like that solution. I was hoping there was a better solution.
For issue #2 the only thing I can think of is using a Contract.Assumes because if I attempt to use Contract.Requires(MyDirectory.Exists || !String.IsNullOrEmpty(MyDirectory.FullName)); it complains about visibility (private field used in a requires on a protected method).