Postdoctoral research gives you a chance to continue your research, establish yourself as an independent researcher in your area, and find new interesting collaborations often outside Sweden. Postdoctoral period is usually situated at a university or a research institute. Use your own contacts and those of your supervisors to find a best postdoc placement for you.
Postdoctoral research is usually funded through scholarships. Here you find some major funders:
Swedish Research Council (Vetenskapsrådet):
Riksbankens Jubileumsfond:
Pro Futura programmet: http://www.rj.se/For-forskare/Pro-Futura/