How to cast object to type known only at runtime

Consider the following situation. I have a Dictionary<string,string> dictionary, and a string key. I do not know these two types at compile time, but I do know them at runtime. So at compile time, they're just objects. I'd like to make the call dictionary.ContainsKey(key). However, because key is a string "cast to an object", this yields a RuntimeBinderException. I'd like to understand how to resolve this issue.

Here are some tests demonstrating the issue:

    [TestMethod]
    public void ThisTestFails()
    {
        dynamic dictionary = getDict();
        var key = getKey();

        bool result = dictionary.ContainsKey(key);
        Assert.IsTrue(result);
    }

    [TestMethod]
    public void ThisTestWorks()
    {
        dynamic dictionary = getDict();
        var key = (string)getKey();

        bool result = dictionary.ContainsKey(key);
        Assert.IsTrue(result);
    }

    private object getDict() => new Dictionary<string, string>() { { "abc", "def" } };
    private object getKey() => "abc";

ThisTestFails fails with a RunTimeBinderException, while ThisTestWorks passes. So, what's happening is that while the key variable in both tests contains a string, its apparent type in ThisTestFails is an object, which can't be used in dictionary.ContainsKey.

What I need to resolve this, essentially, is a way to "cast" the key variable to a string at runtime. The (string)key solution in ThisTestWorks won't be useful to me, as I in the general case don't know the type of the dictionary key at compile time. What can be done to solve the issue?