Trustworthiness is the quality of being someone or something that can be trusted. It is the noun form — the thing itself, not a description of a person. You use it when you are talking about that quality as a subject: a company checks the trustworthiness of a new supplier; a reader questions the trustworthiness of a website; a judge weighs the trustworthiness of a witness. Because it names a quality, it fits naturally after words like question, doubt, prove, assess, and after of. It is a long, formal word, and it belongs in writing more than in speech. In conversation people almost never say it — they say "can we trust them?" instead. You will meet it most in news writing, business reports, school essays, and research about media and information. It works for things as well as people: the trustworthiness of a machine, of a set of figures, of a news source. What it means there is that the thing does what it says it does, again and again, so you can rely on it.