Apple Ultra cellular compatibility between EU and Singapore

Depending on your Apple Watch model, the built in hardware may not support all carriers.

Have a look at the chart in this article:

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To cover the LTE and UMTS bands used around the world, there are two separate cellular models for Apple Watch Series 9, Apple Watch SE and Apple Watch Ultra 2. They have been optimised for use in the country of purchase, and not all models work in all countries or regions. There is no single model that supports cellular service worldwide. To see which network providers in your country or region offer cellular service for Apple Watch, refer to the chart below.

Apple Watch - Carriers - Apple

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copied from: Apple Watch - Network Providers - Apple Support

If your Apple Watch Ultra 2 a model A2986, it should also work in the EU, check the details in the article mentioned above.

The Apple Watch Ultra 2, model A2987 is optimized for the use in China mainland and Hong Kong:

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Apple Watch Ultra 2

• Model A2987

This product has been optimized for use in China mainland and Hong Kong.

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copied from: Apple Watch - Network Providers - Apple Support

You may run into similar issues, buying an iPhone abroad, the built in hardware might not support all carriers and features.

iPhone - Supported 5G and LTE networks - Apple