For a marriage abroad: almost always yes. The authority at your destination generally requires a certified (Germany, Austria) or notarised (Switzerland) translation of your certificate of no impediment or certificate of capacity to marry, often together with an apostille. Which document you need, and who issues it, differs by country — see the comparison below.
The first question to settle, though, is what your own country issues. Ireland, the United Kingdom and Australia issue a certificate of no impediment or letter of freedom — for Australia, the Certificate of No Impediment (CNI), issued by DFAT (the Department of Foreign Affairs and Trade) through the Australian Passport Office or an Australian mission abroad, based on a statutory declaration; the United States issues none, and Canada only a statement in lieu — in those cases, and commonly also for the Australian CNI, the route generally runs via an exemption (Befreiung) from the president of the Oberlandesgericht under § 1309 BGB, and the Standesamt tells you which sworn declaration it will accept alongside it. That decides everything that follows.