diff --git a/spinedb_api/import_mapping/generator.py b/spinedb_api/import_mapping/generator.py
index 1af95d9d..b73037a4 100644
--- a/spinedb_api/import_mapping/generator.py
+++ b/spinedb_api/import_mapping/generator.py
@@ -83,6 +83,7 @@ def get_mapped_data(
     rows = list(data_source)
     if not rows:
         return mapped_data, errors
+    column_count = len(max(rows, key=lambda x: len(x) if x else 0))
     if column_convert_fns is None:
         column_convert_fns = {}
     if row_convert_fns is None:
@@ -92,7 +93,7 @@ def get_mapped_data(
     for mapping in mappings:
         read_state = {}
         mapping = deepcopy(mapping)
-        mapping.polish(table_name, data_header)
+        mapping.polish(table_name, data_header, column_count)
         mapping_errors = check_validity(mapping)
         if mapping_errors:
             errors += mapping_errors
diff --git a/spinedb_api/import_mapping/import_mapping.py b/spinedb_api/import_mapping/import_mapping.py
index 5259a7f1..c07d4f3c 100644
--- a/spinedb_api/import_mapping/import_mapping.py
+++ b/spinedb_api/import_mapping/import_mapping.py
@@ -135,22 +135,44 @@ def read_start_row(self, row):
             raise ValueError(f"row must be >= 0 ({row})")
         self._read_start_row = row
 
-    def polish(self, table_name, source_header, for_preview=False):
+    def check_for_invalid_column_refs(self, header, table_name):
+        """Checks that the mappings column refs are not out of range for the source table
+
+        Args:
+            header (list): The header of the table as a list
+            table_name (str): The name of the source table
+
+        Returns:
+            str: Error message if a column ref exceeds the column count of the source table,
+            empty string otherwise
+        """
+        if self.child is not None:
+            error = self.child.check_for_invalid_column_refs(header, table_name)
+            if error:
+                return error
+        if isinstance(self.position, int) and self.position >= len(header) > 0:
+            msg = f"Column ref {self.position + 1} is out of range for the source table \"{table_name}\""
+            return msg
+        return ""
+
+    def polish(self, table_name, source_header, column_count=0, for_preview=False):
         """Polishes the mapping before an import operation.
         'Expands' transient ``position`` and ``value`` attributes into their final value.
 
         Args:
             table_name (str)
             source_header (list(str))
+            column_count (int, optional)
+            for_preview (bool, optional)
         """
-        self._polish_for_import(table_name, source_header)
+        self._polish_for_import(table_name, source_header, column_count)
         if for_preview:
             self._polish_for_preview(source_header)
 
-    def _polish_for_import(self, table_name, source_header):
+    def _polish_for_import(self, table_name, source_header, column_count):
         # FIXME: Polish skip columns
         if self.child is not None:
-            self.child._polish_for_import(table_name, source_header)
+            self.child._polish_for_import(table_name, source_header, column_count)
         if isinstance(self.position, str):
             # Column mapping with string position, we need to find the index in the header
             try:
@@ -185,6 +207,9 @@ def _polish_for_import(self, table_name, source_header):
             except IndexError:
                 msg = f"'{self.value}' is not a valid index in header '{source_header}'"
                 raise InvalidMappingComponent(msg)
+        if isinstance(self.position, int) and self.position >= column_count > 0:
+            msg = f"Column ref {self.position + 1} is out of range for the source table \"{table_name}\""
+            raise InvalidMappingComponent(msg)
 
     def _polish_for_preview(self, source_header):
         if self.position == Position.header and self.value is not None:
diff --git a/spinedb_api/spine_io/importers/reader.py b/spinedb_api/spine_io/importers/reader.py
index 92eda12f..051618b9 100644
--- a/spinedb_api/spine_io/importers/reader.py
+++ b/spinedb_api/spine_io/importers/reader.py
@@ -16,7 +16,7 @@
 
 from itertools import islice
 
-from spinedb_api.exception import ConnectorError
+from spinedb_api.exception import ConnectorError, InvalidMappingComponent
 from spinedb_api.import_mapping.generator import get_mapped_data, identity
 from spinedb_api.import_mapping.import_mapping_compat import parse_named_mapping_spec
 from spinedb_api import DateTime, Duration, ParameterValueFormatError
@@ -151,7 +151,7 @@ def get_mapped_data(
                     row_convert_fns,
                     unparse_value,
                 )
-            except (ConnectorError, ParameterValueFormatError) as error:
+            except (ConnectorError, ParameterValueFormatError, InvalidMappingComponent) as error:
                 errors.append(str(error))
                 continue
             for key, value in data.items():