If you don't have a paper marriage certificate, you can still use an electronic version of the certificate, but with a number of restrictions. Here's how it works:
When your marriage is registered, you receive an electronic copy of the marriage certificate. Within the United States, an electronic certificate may be sufficient for most administrative purposes, such as changing your name at a bank or applying for a visa.
For international recognition, you will need to order a paper copy of your marriage certificate and have it apostilled by the Utah Secretary of State's office for the document to be recognized abroad.
In most cases, for international use (e.g. for marriage recognition in Poland, Israel or other countries), only a paper marriage certificate with an apostille is required. An electronic certificate will not have legal force in the international context, since it does not have a physical signature or seal.
Summary: An electronic version of the certificate may be useful for local needs in the US, but for international recognition you will still need to obtain a paper copy and have it apostilled.