The name "sword bay" is likely referring to the Ryggen promontory ridge across from the town of Svelvik.
The official blazon is "Gules, a trident Or" (Norwegian: På rød, bunn en gull Neptun-gaffel).
The trident has a tincture of Or which means it is commonly colored yellow, but if it is made out of metal, then gold is used.
At the same time, the motif has a domestic connection because the trident is the same tool that is locally used for eel fishing.
At the time of the municipal dissolution, it was part of the Nord-Jarlsberg prosti (deanery) in the Diocese of Tunsberg.
The narrow Svelvikstrømmen strait is located part-way along the fjord, near the town of Svelvik.
The shortest ferry line in Norway crosses the fjord there, connecting Svelvik to the Hurum peninsula.