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It's great that you are aware of the potential risks that come with exacerbated breeding behaviour and are willing to take measures to prevent your budgies from trying to raise a family.
In most cases by not having any dark, hiding areas nor anything that your budgies can use as a nest will keep their hormones more under control.
Limiting the amount of daylight hours as well as protein intake and rearranging the cage often will also be helpful. For all the detailed information, you can check this link: When We Don't Want Eggs!
Knowing your budgies and how determined they are with wanting to potentially raise a family, you will be in the better place to judge if it's best to keep them separated for a while (at least until their hormones are under control) or not.
If your female budgie is currently in breeding condition (dark brown coloured cere), you can keep her separated from your male till her cere reverts to the creamy white colour (indicating she's out of breeding condition).
Later on, you can place her back with her mate and follow the recommendations on the link.
If despite all measures taken, they are still very much enamoured, then you can house them on separate cages permanently and allow closely supervised out of cage time together, provided no breeding behaviour is exhibited during play time.
During the adjustment period to being apart, you can cover each cage on 3 sides and have some background music on for them in order to limit the anxiety/stress on them. You can also spend one-on-one time with each of your budgies and take this time to strengthen the bond you have with them. In the early stages, you can place one of the cages on a different room and once they are both more settled and used to the new reality, you can then gradually do the re-introductions and place back the cage on the same room depending on how your budgies behave.