The good news is that most pickpockets in Rome are only interested in cash and/or objects they can sell, so usually they just throw away credit cards after they have stolen your wallet. Still, it is of course a big nuisance when this happens, so here are some recommendations
Stolen credit cards Rome
What to do before your credit card is stolen in Rome
Of course it would be best if you could make sure your credit card did not get stolen at all, so there are a number of simple rules to adhere to if you do not wish this to happen. First of all, keep your cards in a safe place. If you don’t think you are going to need your card during the day, leave it at your Rome hotel or your B&B. Secondly, if you feel you have to take it with you, keep it at a safe spot, preferably underneath your clothes.
Before you leave your home country, make sure you have all the relevant information at your disposal, especially the phone numbers you need to call in order to block your cards in case they do get stolen (see the link below). One thing you could do is scan the cards and mail a copy to yourself. Elsewhere on this site you find a list of the major credit card companies in Rome, their phone numbers and offices.
What to do when your credit cards have been stolen
The first action you should undertake is to find a phone, call the credit card company or your bank and have the card(s) blocked. Don’t panic, since most pick-pockets in Rome are very adept (as you will know in case you need this information) at stealing, but usually what they are after is only cash and objects they are able to sell. Credit cards, passports, driver’s licenses and other documents are often just thrown away.
Once you have done this, you will need to go to a Rome police station and report the theft. You will need this for your insurance company.