The information in this article (and other similar news sources available today) is a bit more specific than earlier articles I read about work on vaccination passports. Sweden hopes to "have the infrastructure to issue digital certificates in place by June". The certificates are intended to enable overseas travel. Denmark hasn't publicized a target date for the sort of electronic system that would allow individuals to have vaccine verification on their cell phones but plans to have a low-tech (look-up) system fairly soon ("in late February").
I take this article as an indication of serious intent but do not assume it means I can go to Sweden in June or July.
https://www.ndtv.com/world-news/sweden-denmark-to-develop-digital-covid-vaccine-passports-2363330