Make them pay
If they are working part-time or get pocket money, then you could let them pay it themselves. Suggest that they budget their own money so that they can pay the bill. This would lead to them putting on their own restrictions which they may see as fairer. You could also consider giving them a monthly budget for their phone and then once they go over that not giving them any more money. This will allow them to be able to budget it themselves.
Get a fixed contract
It is possible to have a contract where you can only spend a limited amount of money each month. This means that you will not have to spend more than you want too. It also teaches them about how to spread their phone usage so that they do not spend too much. Explain to them how much time they can use it per week or day so that they do not run out of money before the end of the month.
Turn off the wi-fi
It can be worth turning the wi-fi function off the phone from time to time. This will mean that usage is restricted and therefore so is spending. There are even apps which will do this for you, so that a phone can only be used for roaming, for a certain amount of hours per day or can switch off that function after a certain time at night. They will still be able to phone and text, but at least what they can use the phone for will be limited.
Limit their phone usage
You may just decide that you will limit how much they can use their phone in a day. This will obviously reduce the amount of money that they can spend when they are using it. You may find that you will have to experiment with different time limits to see what works with the monetary budget that you have set.
Give them a landline in their room
If your child is using the phone for calls and spending a lot of money that way, then it could be cheaper to give them access to a landline. It will probably be necessary to make sure that they can talk privately, therefore putting a phone in their room or giving them access to a portable phone. If you already have a free call or cheap call contract for your land line, then this could end up being very much cheaper.