Are you not allowed to carry your handbag? Is there a size that is permissible?
The only place I've had to check a handbag-sized bag was at the Borghese. But their system is excellent, and it's free.
Yes, you can carry your handbag into museums. I assume if you are calling it a handbag (size wise) you are not asking about luggage storage.
Sarah, As previously mentioned, the only place you'll likely have to check your handbag is at the Galleria Borghese in Rome. Just about everything has to be checked there! With at least some of the other Museums and Galleries, you won't necessarily have to check your handbag, but it may have to be put through airport style X-Ray Scanners. As I recall, that's also the case when entering the Vatican and Colosseum. Happy travels!
Depending on the size of the bag and the strictness of the guide you may also need to check your handbag for the scavi tour in Rome. Other than that the only other place I can think of has already been mentioned- the Borghese gallery. Donna
I've not been asked to check my messager-type bag except at the Borghese, but we've often been forced to check a daybag that is backpack style, no matter how small. So we usually stuff my bag and his pockets full, and leave the backpack behind.
The Borghese Gallery may ask you to check your large handbag, but if there is something you want to keep on your person (meds, wallet, even a small bottle of water), they will give you an opaque plastic bag with their logo on it to take into the Gallery with you. Not as tacky as it sounds.