Yeah those little white round balls blend in well with the buds, they are eggs though!
I usually just pick off little bits of the plant that the eggs are attached to and put them in a small container until they hatch. Then help them onto a potted plant if one is available or cuttings of whatever food plants you have. If using cuttings make sure the water container opening is blocked (use tissue or paper or something) so the little cats can't get into the water and drown. The eggs do darken just before hatching but that white color is what they look like at first.
Usually I use a tiny piece of the plant to help the tiny caterpillar out of the container onto his food (you could squash them trying to pick them up).
There is lots of info on this site, but I picked one post below where gcertain did a nice photo documentary of the BST cycle. Great egg pics.

Good luck with them.
Kelly

Here is a link that might be useful: Black Swallowtail

Thanks Kelly, it sounds like the eggs in the 2nd pic might have been laid a few days ago? I definitely witnessed her lay the egg in the 1st pic. How exciting!

It sounds like I bring in the eggs or little cats and raise them similarly to the Monarchs. I used a plastic salad box with holes and paper towel spread on the bottom. I emptied the poop each day, cut fresh Asclepias leaves 1 or 2x per day, and the cuttings seemed to do fine not being in water. The most I raised was 5 fat Monarch cats in 1 box!

Oh dear, I don't know if there is enough to feed the BST cats out there. Better start giving extra water to their host plants! There are some organic farms in the local area if I run out of food. :)

Okay, I just thoroughly clean 2 containers and collected 7 eggs! Yippee! 3 of the eggs are laid today and are fresh and white. 4 of the eggs are brownish and will probably hatch sooner.

Thanks for posting that link, it is a fabulous thread with tons of pictures and information.