Help with? Male and female babies

They need to be separated right now. Three weeks is the longest a baby male can be safe with females.

Most vets want young males to be 350-400 grams before they're neutered, so usually 3-4 months old or so.

We separated them tonight! She was getting territorial with him on our lap.
How will I know if she is pregnant?

We put their "cages" next to each other. Can they have any supervised time together? I am afraid they won't "know" each other after all this time after neutering

No they can't have even supervised time together, guinea pigs can mate in a mater of seconds. You are right they won't really know each other any more after a day or two of not being in the same cage, but supervised time together won't change that. When they are separated they will begin to claim their separate spaces as their own territory, and any guinea pig who is not constantly sharing the territory is an invader, even if they see each other daily it doesn't matter, supervised time together won't help and it opens you up to the risks of her getting pregnant if she isn't already or even them fighting from the stress of having a "foreign" guinea pig near them so regularly.

When it comes time to put them back together once he is 3 to 4 weeks post op from the neuter you will need to introduce them from scratch. See this link for more information on how to properly introduce two guinea pigs https://guinea-pigs.livejournal.com/3002707.html

We have a small cage that we used for a hamster, and a makeshift small dag crate that we are using now. We have ordered a large cage that was to house both of them. Should I wait to use that one until we are ready to introduce them? Or, just clean it really well as instructed?

I added a lid after taking this picture, but this is the set up my supposed "sisters" shared after I realized I had a boy and girl. I got them at a month old and they were fine for the 3 and a half months separated.

Did you have to "reintroduce" them once they could be back together?

I reintroduced them when I visited home (college student). All their stuff was clean and I put them straight into the makeshift cage together... Mine were fine but I didn't really do "proper" introductions...

@Newbabies20 Are you talking about the adults or the babies? Unless one gets fixed, the male and female should never be reintroduced even with lids on the cages. A determined male would climb over the divider with no problem.

@CavyMama I have a male and female baby, about 4 weeks. We have them separated in the same cage--35"x25" separated by 1/4" wire mesh. We have a new, larger cage coming(delayed by shipping). I am hoping to use the same set up, like above picture, until we can get the male neutered.

Once the male is neutered, will we need to reintroduce them, since they have been "together"?