For international travel I recommend at least one chip card, also known as a EMV credit card, these cards have been standard in Europe for years but are only recently available in the US.
Below is a link to a Google spreadsheet that may make your search easier. I have a collection of credit cards and just to check I contacted every card carrier and requested a chip card.
I had a BankAmericard through NCL that I no longer used. When the NCL card arrived with an updated expiration date, I called to activate it. The representative asked me why I no longer used it and I told him I needed a card with a chip. He told me about the BankAmericard Travel Rewards Visa Card, not currently available as a Master Card. I requested the Travel Rewards card with a chip and it arrived a few days later. My credit limit, history and rewards points all remained the same.
I’ve used it exclusively since it came and can see this card going with me on international trips, however it is a Chip and signature not a Chip and pin. So it will not work at unattended locations. There is no fee for international transactions.
When I called to inquire about a PIN for ATM use I was told that there is a 4% cash withdrawal fee and interest accrues upon withdrawal.
Also available were chip cards for American Express but it is still not as widely accepted as Visa and MasterCard and it has a 2.7% foreign transaction fee.
Since I already had credit cards with these companies I just requested a new card with the chip. There are no foreign transaction fees on this card.
Of note, these were not offered or sent as renewal cards and had to be requested.
I do not pay a yearly fee for any of my cards and such providers as Capital One, Chase and Citi do not have chip cards at this time for the no fee cards.