The following are some suggestions to help reduce data usage on your iPhone while traveling. Please keep in mind, even with these suggestions, your phone could still pull some data for System Services. The only way to completely stop data usage is by turning off Data Roaming or keeping your phone on Flight Mode.
1. Disable Automatic App Updates on Cellular Data
Make sure your applications only update over Wi-Fi
Go to Settings > iTunes & App Stores > Turn Off Use Cellular / Mobile Data
2. Disable Background App Refresh
Prevent your applications from pulling data in the background when your not actively using them.
Go to Settings > General > Background App Refresh > Turn it Off entirely or by selective Apps
3. Disable iCloud on Cellular Data
Make sure iCloud is only syncing over Wi-Fi.
Go to Settings > Cellular / Mobile Data > Turn Off iCloud Drive
4. Disable Wi-Fi Assist
Wi-Fi Assist allows you to stay connected when you have a poor Wi-Fi connection. If your traveling and connected to local Wi-Fi (Hotel, Cafe, Restaurant), these Wi-Fi connections may not be reliable and your phone may automatically switch to using data from your KnowRoaming SIM if Wi-Fi Assist is on.
Go to Settings > Cellular / Mobile Data > scroll to bottom > Wi-Fi Assist > turn OFF
For more on WiFi Assist, visit Apple Support: https://support.apple.com/en-ca/HT205296
5. Disable Cellular Data for Unused Apps
Browse through your installed applications and disable unused applications or applications that use a lot of data. Applications disabled from this menu will still function over Wi-Fi.
Go to Settings > Cellular > Scroll through and disable applications you don't want to used your Cellular Data
6. System Services
Please keep in mind, even with the adjustments above, you can still have unexpected data usage from your System Services. You will not be able to disable your System Services and they can be responsible for a lot of unexpected data usage. System Services includes Push Notifications, Time & Location, iTunes Accounts, Software Updates, Mapping Services, Messaging Services, Security Services, Networking, Documents & Sync and more.
Have a look in your iPhone's System Services and you will be able to see the additional usage. (Go to Settings > Cellular / Mobile Data > System Services)