Sweden's history is chequered as it has gone in and out of many Unions with its neighbours Norway and Denmark. Heraldically, this has meant many changes to the Quarterings on its Coat of Arms. Now, the Achievement has reverted to two Quarterings, namely the three Gold Crowns on blue and the Gold Lion on a wavy background ("Bendy wavy Argent and Azure, a lion Or"). Whether you believe the back-histories or not - that the three crowns represent a variety of three different kingdoms or that the golden lion is the Göta Lion - these symbols have represented Sweden since the Middle Ages. They are brought together by a gold cross, said to have been a symbol seen in the sky by 12th-century King Eric IX as he landed in Finland during the First Swedish Crusade.
The small Shield, or Inescutcheon, traditionally carries the Arms of the ruling dynasty - which, in this case, combines Vasa and Bernadotte. That all said (and further enquiries can be made in more depth elsewhere), these Arms are dynastic and national; the Coat of Arms of a head of state.
A different form of Cadency has evolved in Sweden that fits in nicely with these Quarterings. As with other Royal Families, such as the British, Swedish Princes have traditionally been granted dukedoms. The titles have been gleaned from the historic Provinces of Sweden such as Skåne and Värmland. Emerging in the early 19th Century with the establishment of the new dynasty, differencing of Arms was shown by the Prince exchanging one his Quarterings for the Arms of his ducal Province. With the current Royal Family, now daughters have now been allowed into the Succession and therefore have Ducal Titles granted to them in their own right, they also quarter their ducal Province's Coat of Arms. Previously, royal heraldry in Sweden was strictly traditional and old fashioned, so female members were never granted their own Coat of Arms and all simply used those of their father. For instance, the current King's four sisters (The Haga Princesses) all have exactly the same personal Coat of Arms and their Stallplates for the Order of the Seraphim are identical except for their names.
The only fly in the ointment for me, looking back at previous generations's Coats of Arms, has been the positioning of the ducal Province's Arms. Because of the ever-changing Unions and the significance and importance of one country's Arms over another, the positioning has sometimes not only been low in significance but sometimes awkward if not truly awful. Thankfully, this has now settled on the Third Quarter (i.e. lower left). Non-armigerous spouses are granted arms, where necessary, with something personal replacing the dynastic Inescutcheon. (See HM The Queen and HRH Prince Daniel.)
At the moment, HRH Princess Sofia has not been assigned Arms but is expected to carry her husband's as Duchess of Värmland with her personal escutcheon in the middle. Mr Christopher O'Neill (married to HRH Princess Madeleine) has not been created a Prince of Sweden and chooses not to share his wife's title. He does not require a Coat of Arms for any Stallplate as he is not a Knight of any Order of Chivalry; he is 'only' a Commander of the Royal Order of the Polar Star.
My other observation is the use of the Order of the Seraphim. This is granted to all Members of the Royal House, either 'as of birth' (or, more practically speaking, at the baby's christening) or on marriage. The King extended the courtesy to his four sisters as well. According to their Stallplates, male members of the Royal House appear still to be granted the Chain as well as the sash, and HRH Crown Princess Victoria too. However, I have not seen any photographic evidence of the Chain of the Order being worn in recent years by anyone other than The King, except for HRH Prince Carl Philip at his elder sister's wedding. He didn't even wear it at his own wedding in 2015. Either way, though, if they are granted the Chain then that encircles their Shield. If not, then the pale blue Riband with the Star does.
Notice in the gallery below as well the 'system' for how the Ducal Quarterings for Princes and Princesses of the Royal Blood work, and also the Inescutcheons the small shields in the middle) for spouses. I am also including a representation of the Coat of Arms of HRH the late Princess Lilian, Duchess of Halland, not only to show her Arms as the wife of a Royal Duke, but also to show the heraldic pun of her personal Inescutcheon - the representation of a bunch of lilies in honour of her first name rather than her surname...