Lord Dundee is Croatia's honorary consul in Edinburgh, and Lord Grenfell is the secretary of the all-party group for Croatia in the British parliament.
The award-giving ceremony was held in Sponza Palace in the Adriatic resort of Dubrovnik on Saturday morning.
After that, President Josipovic held talks with Croatians who used to be detained in the Morinj prison in Montenegro, during the Serbian and Montenegrin aggression at the south of Croatia in the early 1990s.
During his stay in Dubrovnik, Josipovic also visited the local university.
He described Dubrovnik, which was the venue of the Croatia Summit on Friday and Saturday, as the hub of the political life, tourism and culture.
On Saturday evening, Josipovic and his Slovenian counterpart Danilo Tuerk will attend the ceremony of opening the 61st Dubrovnik Summer Festival.