I am wondering if the Gripsholm Portrait, rather than portraying Queen Elizabeth I of England, is not of Archduchess Maria of Austria (1531–1581), Duchess of Jülich-Cleves-Berg, daughter of Holy Roman Emperor Ferdinand I from the House of Habsburg and Anna of Bohemia and Hungary.
Certainly this is not Elizabethan fashion. The flat little hat is typical Austrian fashion for the time, more specifically typical Austrian fashion for the unhappy daughters of Ferdinand I, Holy Roman Emperor from the House of Habsburg. They are all pictured with it at some point. The straight shapeless gown that does not conform to the contours of the body and the almost too-big overcoat are perfectly in keeping with this style as well. Maria was born on the 15th of May 1531, which means that the portrait would have been painted between the 15th of May 1561 and 16th of May 1562.
1563 Gripsholm portrait thought to be Elizabeth by ? (Gripsholm Slott - Strängnäs, Södermanland Sweden)
Archduchess Maria of Austria, Duchess of Jülich-Cleves-Berg in 1554 – Kunsthistorisches Museum Vienna
Gripsholm Castle – Since Gustav Vasa, Gripsholm has belonged to the Swedish Royal Family and was used as one of their residences until the 18th century. It is now a museum, but it is still considered to be a palace at the disposal of the King and as such it is part of the Crown palaces in Sweden.
The current King of Sweden is directly descended from Maria of Austria (1531–1581), Duchess of Jülich-Cleves-Berg is at least five ways. Through her daughter Marie Eleonore, she was ancestor of Marie Louise of Hesse-Kassel, wife of John William Friso, Prince of Orange therefore ancestor of all the current European monarchs.
This shows how the Swedish King, Carl XVI Gustaf of Sweden, is descended from Marie Louise of Hesse-Kassel, herself the descendant of Maria of Austria (1531–1581), Duchess of Jülich-Cleves-Berg.
An even earlier link between the desendants of Maria of Austria (1531–1581), Duchess of Jülich-Cleves-Berg and the Swedish Royal family was the marriage between Maria Eleonora of Brandenburg (11 November 1599 – 28 March 1655) and King Gustav II Adolph of Sweden. She was Queen of Sweden as the consort of King Gustav II Adolph, the great-granddaughter of Maria of Austria and the mother of Queen Christina of Sweden.
In fact, Gripsholm Castle was the dower residence of Maria Eleonora of Brandenburg as the widow of Gustav Adolph of Sweden, she lived there from 1636 until 1640. In May 1625 she had also given birth to a stillborn son at Gripsholm Castle.
Queen Christina was determined to never marry, and when she abdicated, she left the throne to her cousin Charles X Gustav of Sweden, also a descendant of Maria of Austria (1531–1581), Duchess of Jülich-Cleves-Berg. She was his great-grandmother as well.
His bloodline held the throne until 1751, when Adolf Frederick from the House of Holstein-Gottorp ascended the throne.
He too was a direct lineal ascendant of Maria of Austria (1531–1581), Duchess of Jülich-Cleves-Berg.
Adolf Frederick's grandson Gustav IV Adolf of Sweden married another direct descendant of Maria of Austria (1531–1581), Duchess of Jülich-Cleves-Berg, Frederica of Baden.
Adolf Frederick's bloodline held the throne until 1818. The next king was Jean-Baptiste Jules Bernadotte, the first monarch of the present royal family. In a series of dynastic marriages the Bernadottes would marry into the old bloodlines. Sophia of Nassau (1836–1913) who married Oscar II of Sweden, Victoria of Baden (1862–1930) who married Gustaf V of Sweden, and Princess Sibylla of Saxe-Coburg and Gotha (1908–1972) who married Prince Gustaf Adolf, Duke of Västerbotten, were all direct lineal descendants of Maria of Austria (1531-1581), Duchess of Jülich-Cleves-Berg.
EDITED TO ADD:
Since writing the above, I have come across a photograph of the portrait in a better resolution. It was in fact painted in 1563, making the identification as Elizabeth I Tudor give more sense, as she was naturally precisely 30 years old in 1563.
The fashions are still entirely wrong, however, and I still don't believe that it's her.
When researching this portrait I also considered Catherine Jagiellon (1 November 1526 – 16 September 1583), who was Queen of Sweden at this time, her two sisters, with whom she was close, Anna (18 October 1523 – 9 September 1596) and Sophia (13 July 1522 – 28 May 1575), and her sister-in-law Catherine of Austria (15 September 1533 – 28 February 1572), Queen of Poland, with whom she and her sister Anna were close.
Now, knowing with certainty that the lady was 30 years old in 1563 naturally eliminates both Maria of Austria (1531-1581), Duchess of Jülich-Cleves-Berg and Catherine Jagiellon (1526–1583), Queen of Sweden (and her two sisters) as the sitter.
In 1556, when her sister Sophia married and left for Germany and her mother departed for Italy, Catherine Jagellion and her sister Anna were moved to the Palace of Vilnius by their brother Sigismund II Augustus of Poland, to ensure a royal presence in Lithuania. Their stay in Vilnius was described as happy, living in a palace and a court strongly influenced by the Italian Renaissance: Catherine and Anna were allowed to compose their own separate households, and socialized with the aristocracy. In Vilnius too resided Catherine of Austria, Queen of Poland, their sister-in-law.
It seems that the three women became close. All three had Vilnius as their main place of residence until October 1562 and the wedding of Catherine Jagiellon to Duke John of Finland.
Catherine of Austria was sent to Radom in April 1563 by her 40-year-old husband Sigismund II Augustus of Poland. He sought to obtain annulment of the marriage as he wanted to marry for the fourth time and secure a male heir.
At the same time, between 1563 and 1567, Catherine Jagiellon and her husband John was imprisoned by his brother King Eric XIV in Gripsholm Castle. John's son Sigismund, later the King of Poland and Sweden, was born in Gripsholm Castle on the 20th of June 1566.
Catherine's captivity was a lenient one, however, and if a portrait had been sent to her as a gift at this point she would no doubt have been allowed to receive it. King Eric XIV had no desire to offend either Catherine's family.
It was a time of great turmoil for both Catherines, as well as being shortly after they had been separated in October 1562, after six years as friends and family in each other's close vicinity. Catherine of Austria, Queen of Poland must have been worried both for her own future and quite possibly for the safety of Catherine Jagellion, Queen of Sweden in her captivity.
People have done stranger things under such circumstances than to send a portrait of themselves to be remembered by, as a solace in the form of an offering of remembered friendship and familial love in a difficult situation, and in order to confirm bonds of kinship.
Catherine of Austria (1533–1572), Queen of Poland was also the two years younger sister of Maria of Austria (1531–1581), Duchess of Jülich-Cleves-Berg.
Above is outlined very clearly how the Gripsholm Portrait if a portrait of the childless Catherine of Austria could have come to Sweden by way of inheritance through the descendants of her sister Maria, if it were not in fact a gift to her treasured sister-in-law Catherine Jagiellon (1526–1583), who was Queen of Sweden and actually living at Gripsholm Castle in 1563.