A marriage ceremony in Sweden can take place either in a church or before a civil authority. The Marriage Code and other statutes involving spouses is gender-neutral.
Before the ceremony you need to get a marriage license from the local Swedish Tax Agency in the area where the wedding is taking place. It is essential to contact the Tax Agency well in advance since you must visit in person. The procedure can take some time and you need to make sure that you have the correct documents. Your marriage licence is valid for four months from the date of issue
The Swedish Tax Agency's website
In order to apply for a marriage license British citizens living in the UK need to obtain a Certificate of No Impediment from their local Registry Office. Citizens from other countries need to provide documentation that they are free to marry according to the laws of their home country.
Swedish citizens registered as living abroad and getting married in Sweden must apply for their marriage license in Sweden. A Swedish citizen/other non UK citizen who has lived in the UK for a longer period of time might be asked by the Swedish Tax Agency to produce an additional certificate of civil status, a No trace of Marriage. The certificate is issued by the General Register Office.
The General Register Office's website
If the parties wish to get married in a church before a vicar, they should contact the vicar well in advance for information on what is required and to make the necessary arrangements. A marriage in a church belonging to the Church of Sweden is a legally valid ceremony.
The Church of Sweden's webiste
The Local County Administrative Boards appoint the civil marriage officiants. Swedish civil marriage officiants are appointed by the local County Administrative Boards.
List of County Administrative Boards
In Stockholm, a marriage can take place at the Stockholm City Hall.
More information at Stockholm City Hall's website