Tim mentioned formal exams. This is very good up to the equivalent of a highly skilled, advanced high school student. But an experienced adult musician can very easily surpass what is needed to get high marks on an exam, especially if they studied music intensively when they were young. Here are a couple of alternatives if that's your situation, or if you aren't somewhere exams are easily available.
1) Play in a local orchestra, and judge yourself against the players there. Auditions will give you a chance for your skill to be assessed by the people listening. Keep auditioning for higher skill ensembles, and more challenging roles as you continue to learn. This will work best if you are in a metropolitan area with a tradition of high level amateur orchestras. Otherwise, you may have only one to choose from, or none.
2) Get a teacher who is understanding of your goals, and can periodically put together a formal assessment of your abilities, and how much you've improved since the last one. For such a report to be reliable, it should be a good teacher, and someone you take lessons from regularly (not necessarily weekly).
3) Learn to accurately assess your own abilities. This is absolutely key if you want to progress beyond an advanced student level. By doing this, you will be able to pick something you want to play, and figure out which of your skills aren't up to the task. Then focus on improving those skills. You'll have a measure of your improvement in how much better you sound after mastering the piece than before. This should be something you do no matter what route you take with outside feedback, because outside feedback is occasional, but what you give yourself is constant.