diff --git a/cwltool/process.py b/cwltool/process.py
index 44cacec57..56dedea56 100644
--- a/cwltool/process.py
+++ b/cwltool/process.py
@@ -467,6 +467,26 @@ def avroize_type(
     return field_type
 
 
+def _type_contains_file(
+    field_type: CWLObjectType | MutableSequence[Any] | CWLOutputType | None,
+) -> bool:
+    """Return True if a (possibly compound/nullable) parameter type includes a ``File``."""
+    if isinstance(field_type, str):
+        # handle plain ("File"), namespaced ("...#File") and avro ("...cwl.File") forms
+        return field_type.replace("#", ".").split(".")[-1] == "File"
+    if isinstance(field_type, MutableSequence):
+        return any(_type_contains_file(entry) for entry in field_type)
+    if isinstance(field_type, MutableMapping):
+        if field_type.get("type") == "array":
+            return _type_contains_file(cast(CWLOutputType, field_type.get("items")))
+        if field_type.get("type") == "record":
+            return any(
+                _type_contains_file(cast(CWLObjectType, fld).get("type"))
+                for fld in cast(MutableSequence[Any], field_type.get("fields", []))
+            )
+    return False
+
+
 def get_overrides(overrides: MutableSequence[CWLObjectType], toolid: str) -> CWLObjectType:
     """Combine overrides for the target tool ID."""
     req: CWLObjectType = {}
@@ -655,6 +675,14 @@ def __init__(self, toolpath_object: CommentedMap, loadingContext: LoadingContext
                 else:
                     c["type"] = c["type"]
 
+                if "format" in c and not _type_contains_file(c["type"]):
+                    _logger.warning(
+                        SourceLine(i, "format", str).makeError(
+                            "'format' is only valid for 'File' type parameters, but "
+                            "'%s' is not a File; the 'format' field will be ignored." % c["name"]
+                        )
+                    )
+
                 c["type"] = avroize_type(c["type"], c["name"])
                 if key == "inputs":
                     cast(list[CWLObjectType], self.inputs_record_schema["fields"]).append(c)
diff --git a/tests/test_validate.py b/tests/test_validate.py
index 8e664d9aa..4508bd973 100644
--- a/tests/test_validate.py
+++ b/tests/test_validate.py
@@ -57,6 +57,34 @@ def test_validate_with_invalid_input_object() -> None:
     )
 
 
+def test_validate_warns_on_format_for_non_file() -> None:
+    """`format` on a non-File parameter (e.g. Directory) warns but still validates (#1616, #607)."""
+    custom_log = io.StringIO()
+    handler = logging.StreamHandler(custom_log)
+    handler.setLevel(logging.DEBUG)
+    exit_code, _, _ = get_main_output(
+        ["--validate", get_data("tests/wf/format-on-directory.cwl")],
+        logger_handler=handler,
+    )
+    log_text = re.sub(r"\s\s+", " ", custom_log.getvalue())
+    assert exit_code == 0
+    assert "'format' is only valid for 'File' type parameters" in log_text
+    assert "'indir' is not a File" in log_text
+
+
+def test_validate_no_format_warning_for_file() -> None:
+    """`format` on a File parameter is valid and must not warn (#1616, #607)."""
+    custom_log = io.StringIO()
+    handler = logging.StreamHandler(custom_log)
+    handler.setLevel(logging.DEBUG)
+    exit_code, _, _ = get_main_output(
+        ["--validate", get_data("tests/wf/format-on-file.cwl")],
+        logger_handler=handler,
+    )
+    assert exit_code == 0
+    assert "'format' is only valid" not in custom_log.getvalue()
+
+
 def test_validate_quiet() -> None:
     """Ensure that --validate --quiet prints the correct amount of information."""
     exit_code, stdout, stderr = get_main_output(
diff --git a/tests/wf/format-on-directory.cwl b/tests/wf/format-on-directory.cwl
new file mode 100644
index 000000000..184df95b3
--- /dev/null
+++ b/tests/wf/format-on-directory.cwl
@@ -0,0 +1,13 @@
+#!/usr/bin/env cwl-runner
+# Regression fixture for https://github.com/common-workflow-language/cwltool/issues/1616
+# (and #607): `format` is only meaningful for File parameters. Specifying it on a
+# Directory input should produce a validation warning, not pass silently.
+cwlVersion: v1.2
+class: CommandLineTool
+inputs:
+  indir:
+    type: Directory
+    format: http://edamontology.org/format_1915
+    inputBinding: {}
+outputs: []
+baseCommand: echo
diff --git a/tests/wf/format-on-file.cwl b/tests/wf/format-on-file.cwl
new file mode 100644
index 000000000..6417f7561
--- /dev/null
+++ b/tests/wf/format-on-file.cwl
@@ -0,0 +1,11 @@
+#!/usr/bin/env cwl-runner
+# Companion fixture: `format` on a File input is valid and must NOT warn.
+cwlVersion: v1.2
+class: CommandLineTool
+inputs:
+  inf:
+    type: File
+    format: http://edamontology.org/format_1915
+    inputBinding: {}
+outputs: []
+baseCommand: echo