NUnit 3.0 and Assert.Throws

You can create a custom Attribute in NUnit 3. Here is the sample code how to create [ExpectedException] Attribute.(ExpectedExceptionExample Shows how to implement a custom attribute for NUnit) https://github.com/nunit/nunit-csharp-samples

I see where you're coming from, even though I don't mind combining Act/Assert steps in this case.

The only thing I can think of is to store the actual delegate (here to FromPrinergyDateTime) into a variable as the "act" step and then assert it:

[Test]
public void Should_not_convert_from_prinergy_date_time_sample2()
{
    //Arrange
    string testDate = "20121123120122";

    //Act
    ActualValueDelegate<object> testDelegate = () => testDate.FromPrinergyDateTime();

    //Assert
    Assert.That(testDelegate, Throws.TypeOf<FormatException>());
}

I get that the "act" step isn't really acting, but rather defining what the action is. However, it does clearly delineate what action is being tested.

In C# 7, there is another option (albeit very similar to the existing answers):

[Test]
public void Should_not_convert_from_prinergy_date_time_sample2()
{
    void CheckFunction()
    {
        //Arrange
        string testDate = "20121123120122";

        //Act
        testDate.FromPrinergyDateTime();
    }

    //Assert
    Assert.Throws(typeof(Exception), CheckFunction);
}

Blog post on the subject