Materials used:
2.0 g sodium alginate
200 g water (with low calcium content!)
50 g blueberry syrup

2.5 g calcium chloride
500 g water

Procedure:
2 g sodium alginate and 200 g water were mixed vigourously in blender. The mixture was then left to stand for some hours to get rid of the air bubbles. 50 g blueberry syrup was then added to the sodium alginate solution. A calcium chloride bath was prepared by dissolving 2.5 g calcium chloride in 500 g water. The sodium alginate/blueberry mixture was dripped into the calcium chloride bath using a plastic syringe with a steel cannula. After 1-3 min the pearls were removed and rinsed with water.

More detailed procedure with pictures and video:
I had to obtain a scale with a 0.1 g accuracy to weigh out 2.0 g of sodium alginate (my first experiments using a normal kitchen scale failed). The model I got cost about $100 and is inteded for school laboratories. Amazon provides several scales with this accuracy.

I used a blender to dissolve sodium alginate in water. This incorporates a lot of air in the mixture which we don’t want. It could possibly be avoided by using an immersion blender/mixer. However, I just left the alginate solution on the bench and after 3-4 hours the air bubbles had all escaped from the solution.

Plastic syringes and cannulas can be obtained from your local drug store or pharmacist. I found it was easier to produce evenly sized drops with a sharp cannula (CAREFULL!) than with just the plastic tip of the syringe. This of course depends on the viscosity of the solution. By thickening (with xanthan for instance) you can produce larger drops.

After 1-3 min the spheres were removed from the calcium chloride solution and rinsed with clean water. I dried the spheres carefully using a kitchen towel or paper.

Definitely looks like caviar when presented on a spoon like this!

Larger spheres were made by filling a small measuring spoon with the alginate mixture (I used a syringe for this so the outsides of the spoon would not be covered with alginate solution) and carefully emptied it into the calcium chloride bath. It takes some trial and error to achieve good results.

The spheres are suprisingly robust and can be handled without rupturing.

If cut with a knife, the spheres rupture and the liquid contents flows out.

The small spheres didn’t taste much, so I could have added more blueberry syrup. The large spheres however had a nice taste. The surprise element when they rupture in your mouth is very nice!