Good question!

What I do (when I think it's important to distinguish synonyms) is add the synonyms to the English-prompt side of the card.

My convention is to read the synonym quickly along with the English prompt, like so: "as soon as she comes; tan pronto como."

This works best for isolated nouns or verbs, such as "the frame, montura --> el marco". Here are examples of how I used to do it (before I started using audio cards): https://imgur.com/a/u9Zes0Q

It doesn't work as well for more complex constructs that have many direct synonyms (I've given up on having a sharp card for "however," for example---there's just too many ways to say it in Spanish: "sin embargo," "de todas maneras," "de todos modos," etc.).

For longer sentence fragments, I often don't bother to distinguish synonyms. As long as I can produce one Spanish translation that I know is correct, I'll let it pass. If it's hard to make a concise prompt for production, I'll settle for recognition practice.