Understand liability insurance.
Be sure that the program you are working with provides liability insurance for its mentors and that you fully understand the extent of your liability and dimensions of any coverage that is offered. Strong mentoring programs cover this subject in mentor orientation sessions. If your program or program coordinator does not do so, raise the question and get an answer that satisfies you. There are very, very cases in which the mentee or the mentee’s family sues mentors (in both instances, very sadly, the suits related to sexual harassment or assault), but that doesn’t mean you should feel released from the obligation of understanding the liability issue. Doing so is likely to ease rather than exacerbate concerns, since you are likely to find that the liability issues that most worry mentors (e.g., that their mentee will be hurt in an accident in their company) rarely occur and are almost always covered by either the program or your personal liability insurance, which most adults now have.