diff --git a/autotest/gdrivers/jp2openjpeg.py b/autotest/gdrivers/jp2openjpeg.py
index 8ecddf3bd252..51f93b4848aa 100755
--- a/autotest/gdrivers/jp2openjpeg.py
+++ b/autotest/gdrivers/jp2openjpeg.py
@@ -3864,3 +3864,62 @@ def test_jp2openjpeg_limit_resolution_count_from_image_size(tmp_vsimem):
     # Check number of resolutions
     ret = gdal.GetJPEG2000StructureAsString(filename, ["ALL=YES"])
     assert '<Field name="SPcod_NumDecompositions" type="uint8">2</Field>' in ret
+
+
+###############################################################################
+# Test unsupported XML SRS
+
+
+def test_jp2openjpeg_unsupported_srs_for_gmljp2(tmp_vsimem):
+
+    filename = str(tmp_vsimem / "out.jp2")
+    # No EPSG code and Albers Equal Area not supported by OGRSpatialReference::exportToXML()
+    wkt = """PROJCRS["Africa_Albers_Equal_Area_Conic",
+    BASEGEOGCRS["WGS 84",
+        DATUM["World Geodetic System 1984",
+            ELLIPSOID["WGS 84",6378137,298.257223563,
+                LENGTHUNIT["metre",1]]],
+        PRIMEM["Greenwich",0,
+            ANGLEUNIT["degree",0.0174532925199433]],
+        ID["EPSG",4326]],
+    CONVERSION["Albers Equal Area",
+        METHOD["Albers Equal Area",
+            ID["EPSG",9822]],
+        PARAMETER["Latitude of false origin",0,
+            ANGLEUNIT["degree",0.0174532925199433],
+            ID["EPSG",8821]],
+        PARAMETER["Longitude of false origin",25,
+            ANGLEUNIT["degree",0.0174532925199433],
+            ID["EPSG",8822]],
+        PARAMETER["Latitude of 1st standard parallel",20,
+            ANGLEUNIT["degree",0.0174532925199433],
+            ID["EPSG",8823]],
+        PARAMETER["Latitude of 2nd standard parallel",-23,
+            ANGLEUNIT["degree",0.0174532925199433],
+            ID["EPSG",8824]],
+        PARAMETER["Easting at false origin",0,
+            LENGTHUNIT["metre",1],
+            ID["EPSG",8826]],
+        PARAMETER["Northing at false origin",0,
+            LENGTHUNIT["metre",1],
+            ID["EPSG",8827]]],
+    CS[Cartesian,2],
+        AXIS["easting",east,
+            ORDER[1],
+            LENGTHUNIT["metre",1,
+                ID["EPSG",9001]]],
+        AXIS["northing",north,
+            ORDER[2],
+            LENGTHUNIT["metre",1,
+                ID["EPSG",9001]]]]"""
+    gdal.ErrorReset()
+    assert gdal.Translate(
+        filename, "data/byte.tif", outputSRS=wkt, format="JP2OpenJPEG"
+    )
+    assert gdal.GetLastErrorMsg() == ""
+    ds = gdal.Open(filename)
+    ref_srs = osr.SpatialReference()
+    ref_srs.ImportFromWkt(wkt)
+    assert ds.GetSpatialRef().IsSame(ref_srs)
+    # Check that we do *not* have a GMLJP2 box
+    assert "xml:gml.root-instance" not in ds.GetMetadataDomainList()
diff --git a/frmts/opjlike/jp2opjlikedataset.cpp b/frmts/opjlike/jp2opjlikedataset.cpp
index f044b0644f9e..ccef0e8a0ec6 100644
--- a/frmts/opjlike/jp2opjlikedataset.cpp
+++ b/frmts/opjlike/jp2opjlikedataset.cpp
@@ -2471,10 +2471,18 @@ GDALDataset *JP2OPJLikeDataset<CODEC, BASE>::CreateCopy(
             {
                 bGeoreferencingCompatOfGeoJP2 = TRUE;
                 oJP2MD.SetGeoTransform(adfGeoTransform);
+                if (poSRS != nullptr && !poSRS->IsEmpty())
+                {
+                    bGeoreferencingCompatOfGMLJP2 =
+                        GDALJP2Metadata::IsSRSCompatible(poSRS);
+                    if (!bGeoreferencingCompatOfGMLJP2)
+                    {
+                        CPLDebug(
+                            CODEC::debugId(),
+                            "Cannot write GMLJP2 box due to unsupported SRS");
+                    }
+                }
             }
-            bGeoreferencingCompatOfGMLJP2 =
-                poSRS != nullptr && !poSRS->IsEmpty() &&
-                poSrcDS->GetGeoTransform(adfGeoTransform) == CE_None;
         }
         if (poSrcDS->GetMetadata("RPC") != nullptr)
         {