The parish church records would record deaths/burials.
The Digitalarkivet web site has been adding scanned images of the original Norwegian parish church records for anyone with Internet access since November 2005. It looks like the death records for Sarpsborg are available as late as 1949 for your use there.
The Digitalarkivet web site - http://digitalarkivet.uib.no/cgi-win/WebFront.exe?slag=vis&a...
An English option is available by clicking on that word from either the left hand column or the blue link bar along the bottom of the homepage.
The scanned images are available from the homepage link "Skanna kyrkjebøker" [Norwegian version]/"Digitised parish records" [English version] which is listed along the left hand column and from the blue banner of links along the top section of the homepage.
Clicking on "Skanna kyrkjebøker" [Norwegian version]/"Digitised parish records" [English version] will bring up another screen and listing to choose from. Choose "Lesa skanna kyrkjebøker" [Norwegian version]/"Read the digitised parish records" [English version].
After you've clicked on that link and a new main page has presented on the screen be sure and read the instructions that are available from the Digitalarkivet for navigating the scanned records. The instructions are available in Bokmål (official Norwegian), Nyorsk (Norwegian), Davvisámegiella (Saami), and English.
Recommended basic reading are the "Startsiden" [Norwegian version]/"Main page" [English version], "Brukerveiledning" [Norwegian version]/"User's guide" [English version] and "Om tjenesten" [Norwegian version]/"About this service" [English version].
Good information about translating the formats of Norwegian parish church records during various time periods, many of the basic terms used and understanding how to use the information should be studied at this web site -http://homepages.rootsweb.com/~norway/na20.html
The family appears in Sarpsborg for the 1900 Norwegian census - http://www.rhd.uit.no/folketellinger/ftliste_e.aspx?ft=1900&...
and in the 1910 -http://www.rhd.uit.no/folketellinger/ftliste_e.aspx?ft=1910&...
So you wouldn't start looking for death records until AFTER those censuses.