Choosing references who will actually help
The most senior person who knows your name is rarely the most useful referee.
A strong reference can speak specifically about work you did. Someone who supervised you closely on a relevant project is more persuasive than a senior figure who can only confirm employment dates, however impressive the title.
Ask first, every time, and ask whether they can speak positively rather than simply whether they are willing. Giving somebody the opportunity to decline gracefully avoids a lukewarm reference, which does more harm than a missing one.
Brief them properly: the role, the organisation, what the employer is likely to ask about, and which parts of your work are most relevant. A referee who knows what is being tested gives a far more useful answer.
Keep them informed of the outcome. People who hear nothing after agreeing to help are less willing the next time, and most careers need the same referees more than once.
Still have a question?
Describe what you are trying to work out and a member of the team will answer, or direct you to the office that makes the decision.