Defined by Wikipedia: "Cerulean, also spelled caerulean, is a color term that may be applied to certain colors with the hue ranging roughly between blue and cyan, overlapping with both. It also largely overlaps with azure and sky blue, although cerulean is dimmer." The inks so classed are generally on the darker side and not like the sky colors, unless toward the end of day but before the pinks and purples of sunset. I am no expert. They exhibit a certain blue brilliance rather than the darker aspect of the blues, graying waters or storms or gathering darkness.
The two that I find to be exceptional are Noodler's Midway Blue and Pilot Iroshizuku Kon-peki. The Midway has a bit of green to it, perhaps less deep waters, while the Iroshizuku is definitely a deep sea blue. They both share a vibrancy of the sea, and I have had people comment on the attractive color of both inks. They behave well, and I will leave it to others to do proper reviews.
The examples above were on Springhill Vellom Bristol-cover Plus 16000 custom cut 3 X 5 cards written with an Esterbrook Jackson Stub #442 in a Koh-I-Noor #127 dip pen in my usual bad handwriting.