There is also risk of your losing them, with all the packing and unpacking, it happens.

I too have taken good jewelry (American spelling) on every trip I have taken to Europe and never had a concern. The rings I never take off. The diamond drop necklace or pearls were either around my neck or in the safe in my room. None of these items is extremely large or ostentatious, and I never felt unsafe. Also, the necklaces I only wore at night in good, well-lit neighborhoods and didn't use public transit. If you want to take them, do.

Do whatever you'd do on a trip to New York City or Washington DC. What do you think the people who live in Rome & Florence do?