abstractTestClass.cs

public abstract class AbstractTestBaseClass
{
    protected MyAbstractClass AbstractedVariable;
    [Fact]
    public void Should_return_correct_message()
    {
        var result= AbstractedVariable.MyMethodOnAbstractClass("input");
        Assert.Equal("I like input in an abstract sense.", result);
     }
}

public class TestingAConcreteClass :AbstractTestBaseClass
{
    MyConcreteClass ConcreteclassUnderTest;
    public TestingAConcreteClass()
    {
        AbstractedVariable = new MyConcreteClass();
        ConcreteclassUnderTest = new MyConcreteClass();
    }

    [Fact]
    public void Should_say_Hello()
    {
        //this is less than ideal as we need to cast to concrete class each time
        var result =  ((MyConcreteClass) AbstractedVariable).SayHello();
        Assert.Equal("Hello", result);
    }

    [Fact]
    public void StillShould_say_Hello()
    {
        //this is better although in constructor we still have 
        //to construct a variable for the abstract tests.
        var result = ConcreteclassUnderTest.SayHello();
        Assert.Equal("Hello", result);

    }

}

public class MyConcreteClass : MyAbstractClass
{
   public string SayHello()
   {
       return "Hello";
   }
}

public class MyAbstractClass
{
    public string MyMethodOnAbstractClass(string input)
    {
        return "I like " + input + " in an abstract sense.";
    }
}