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; the United States issues none, and Canada only a statement in lieu — in those cases 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.
If a UK-issued certificate is what your Standesamt wants, ask your local register office what it will issue and on what basis before you order anything — the practice is set locally. Where no usable certificate is available, the route is the exemption (Befreiung) from the president of the Oberlandesgericht under § 1309 BGB described above, and the Standesamt tells you which sworn declaration it will accept alongside it.