The royal jewels are adorned with gold, precious stones and pearls, and come from the 1611 funeral regalia of Sweden's Charles IX and Kristina the Elder.
Police spokesperson Thomas Agnevik said: "It's too hard to translate these things into some kind of value ..." The two crowns are the burial crowns from 1611 but were later exhumed and put on display.
There is even no definitive description of what the thieves' "small and open motorboat", which the police are searching for, looks like. We are now examining all the tips we receive. "And I told the girls to call the police", he said.
"By boat you can reach Mälaren, Köping or Arboga in the west, or Västerås, Eskilstuna or Stockholm if you drive east".
Two men reportedly lifted them from locked glass boxes and made their getaway in a speedboat waiting at a nearby waterway.
He said: "I have talked to a person at the county administrative board that says that it is not possible to put an economic value on this, these are invaluable objects of national interest".
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"We are spreading out in all directions".
A witness, who is getting married in the Strängnäs Cathedral next week, told local news channel Aftonbladet he contacted the police. Pictured left: The grave of Karl IX at the cathedral. "It's despicable that people would steal from a holy building and a historical building".
Police have mobilised a huge search operation to find the men and recover the items but have so far been unsuccessful.
Nobody was hurt during the raid.
Thieves have made off with priceless Swedish crown jewels, in a daring heist reminiscent of a Hollywood movie.