In my opinion, you should put off your contact lenses. Because as we all know, before buying a eyeglasses, especially the prescription eyeglasses, the pros will ask us to take a eye exam, which can help the expert to know the specific details about our eyes, then they will offer us the right eyeglasses. Everyone knows that there is a "E table" that can check our prescription. If you wear your contact lenses, then the result you get from the exam will not be exact, the worst result is that the eyeglasses you buy can not help you any more because you can not still see clearly wearing the eyeglasses without the contacts.
There are two main types of eye examination that are eye examination and contact lens examination. Whether you wear your contact lenses depend on which type of exam you are having. An eye examination is checking your eyesight and your eye health. A contact lens examination is finding out how well your eyes within the contact lenses. If you wanna purchase a pair of eyeglasses, you have to remove your contact lenses two hours before the appointment, thus your eyes can return to relaxed state. It could help you to know the right eye prescription and whether you have other eye problems.
Of course, you should take off eyeglasses and take the eye exam. The eye exam will check the real vision of your eyes and exact situation of your eyes. Only after you take off the contact lenses can you give the real result of your eye exams. Thus, you'd better remove the contact lenses to check your prescription which may be known for your eyeglasses.