Go back to court and get a court order allowing you access, supervised by the police, to get your things. Have a specific list of items you want to get. A judge would normally allow you a short period of time to get your items as long as the police are present.
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Besides an attorney you cannot have someone else contact the protected person on your behalf as it violates the order. You need either a court order or the person simply offer it to you.
This is just my opinion and not a comprehensive answer. You assume the risk because this answer may not apply to your situation depending on the facts.
It is important to remember that you can be in violation of a no contact order even if you use a friend or third party "agent" to make the contact with the protected party. Please be very careful about having others contact the other side for any reason.
I strongly encourage you to file a motion for inspection of the residence and supervised removal of your personal property from the premises. Having an officer present to keep the peace and act as a witness is always the best recourse, but you should obtain the court's permission first to protect yourself from a contempt motion for violating the protective order.
Most no-contact orders are part of a domestic violence restraining order and such orders prohibit you from having direct OR indirect contact with the other party. Therefore, getting a friend to do it will likely violate the no-contact order against you and that could subject you to contempt. The smart move is to have a lawyer handle this for you. If your ex-wife is represented, we could get in touch with her lawyer and effectuate this. If she is not, we could get in touch with directly her and make this happen for you.
The answer to this question assumes that the no-contact order is a standard order that does not allow direct or indirect contact, such as a domestic violence protective order.