Scandinavian food isn't represented in Shanghai very well. In fact, other than the Ikea Cafe, there is not a dedicated restaurant that represents the furthers northern portion of Europe very well. There are, however, great fusion European restaurants and great seafood restaurants. If you blend the two you may have something bordering Scandinavian fare.
The Ikea Cafe actually serves quite decent food. You'll love the meatballs, and once you are done shopping there are Scandinavian brats and buns that are extremely popular (and incredibly cheap!) Although most people hate shopping there, the items are good and the Ikea Cafe makes it worth the trip.
M on the Bund, Laris and T8 are high-end European restaurants that claim to have a broad range of European cuisines that could include foods from their brethren to the north. These are great bets for fancy nights on the town where you'll want to see and be seen.
Slightly more laid back, Sasha's and the Whampoa Club offer European fusions with a touch of class but without the same cost factor. And even if you don't find anything Scandinavian on the menu you may not care after these great meals.
Scandinavian food involves seafood, and in that vain although you may not find ludafisk, you can get great sushi at Oyama Sushi and great creatures from the deep at the Fortuna Seafood Restaurant.
126 Caoxi Bei Lu, Near Sanhui Lu
Swedish cafe in the IKEA building... read more
7/F, No. 5 The Bund
Modern cuisine with an old-fashioned view and renown atmosphere... read more
11 Dongping Lu
Corner of Heng Shan Lu
Colonial Style Dinning at extreme prices with comfort in style... read more
6/F 3 Zhong Shan Dong Yi Lu
Near Guangdong Lu
Fine Dining with a famous chef and astonishing view... read more
Bailing Lu 23
Corner of Jiujiaochang Lu
Vegans rejoice! A center for like-minded eaters in Yu Yuan... read more
124 Jinxian Lu
Quaint restaurant with no menu and only 4 tables...
Lane 181 Tai Cang Road
8 Xintiandi North Part
3 Zhong Shan Dong Yi
Three on the Bund
111 Tian Mu Xi Lu
3F East China Hotel
Near the railway station, the best fish in town...
20 Donghu Lu, 2F
Near Huaihai Lu
Sushi done perfectly, prices that wont make you cry... read more