Use a payphone. This option seems fairly simple however; you may have over looked it. Payphones may seem obsolete now-a-days. Nevertheless, if you need to call a person that has blocked your number, a payphone may be the way to go. Most people have caller ID. If they receive a call from a payphone, they may be more than likely to answer considering they have no idea who is calling.

Borrow a neighbors or friends phone. This could be their cell or house number. Explain to them that you really need to get a hold of this person and ask if you can use their phone. If the person you are borrowing the phone from has a private name/number, this is an added bonus.

Purchase a cell phone. You can buy a cell that has prepaid minutes or a contract phone. If you just need to call the person that has blocked your number, a prepaid cell may be the least expensive option. When you opt for a contract cell phone, be sure that you request privacy options.

Contact your phone company. For a small fee you can have your number changed and request privacy settings for your number or name will not show up on their caller ID. When you have to call someone that has blocked your number, this solution can assist you greatly.