diff --git a/aiida/engine/processes/calcjobs/calcjob.py b/aiida/engine/processes/calcjobs/calcjob.py
index 3b07181678..2dad3a1ea6 100644
--- a/aiida/engine/processes/calcjobs/calcjob.py
+++ b/aiida/engine/processes/calcjobs/calcjob.py
@@ -396,6 +396,29 @@ def prepare_for_submission(self, folder: Folder) -> CalcInfo:
         """
         raise NotImplementedError()
 
+    def _setup_metadata(self, metadata: dict) -> None:
+        """Store the metadata on the ProcessNode."""
+        computer = metadata.pop('computer', None)
+        if computer is not None:
+            self.node.computer = computer
+
+        options = metadata.pop('options', {})
+        for option_name, option_value in options.items():
+            self.node.set_option(option_name, option_value)
+
+        super()._setup_metadata(metadata)
+
+    def _setup_inputs(self) -> None:
+        """Create the links between the input nodes and the ProcessNode that represents this process."""
+        super()._setup_inputs()
+
+        # If a computer has not yet been set, which should have been done in ``_setup_metadata`` if it was specified
+        # in the ``metadata`` inputs, set the computer associated with the ``code`` input. Note that not all ``code``s
+        # will have an associated computer, but in that case the ``computer`` property should return ``None`` and
+        # nothing would change anyway.
+        if not self.node.computer:
+            self.node.computer = self.inputs.code.computer  # type: ignore[union-attr]
+
     def _perform_dry_run(self):
         """Perform a dry run.
 
diff --git a/aiida/engine/processes/process.py b/aiida/engine/processes/process.py
index 827f115a25..1cc9e87fd6 100644
--- a/aiida/engine/processes/process.py
+++ b/aiida/engine/processes/process.py
@@ -11,6 +11,7 @@
 import asyncio
 import collections
 from collections.abc import Mapping
+import copy
 import enum
 import inspect
 import logging
@@ -684,27 +685,22 @@ def _setup_db_record(self) -> None:
             elif isinstance(self.node, orm.WorkflowNode):
                 self.node.base.links.add_incoming(parent_calc, LinkType.CALL_WORK, self.metadata.call_link_label)
 
-        self._setup_metadata()
+        self._setup_metadata(copy.copy(dict(self.inputs.metadata)))
         self._setup_inputs()
 
-    def _setup_metadata(self) -> None:
+    def _setup_metadata(self, metadata: dict) -> None:
         """Store the metadata on the ProcessNode."""
         version_info = self.runner.plugin_version_provider.get_version_info(self.__class__)
         self.node.base.attributes.set_many(version_info)
 
-        for name, metadata in self.metadata.items():
+        for name, value in metadata.items():
             if name in ['store_provenance', 'dry_run', 'call_link_label']:
                 continue
 
             if name == 'label':
-                self.node.label = metadata
+                self.node.label = value
             elif name == 'description':
-                self.node.description = metadata
-            elif name == 'computer':
-                self.node.computer = metadata
-            elif name == 'options':
-                for option_name, option_value in metadata.items():
-                    self.node.set_option(option_name, option_value)
+                self.node.description = value
             else:
                 raise RuntimeError(f'unsupported metadata key: {name}')
 
@@ -716,10 +712,6 @@ def _setup_inputs(self) -> None:
             if node is None:
                 continue
 
-            # Special exception: set computer if node is a remote Code and our node does not yet have a computer set
-            if isinstance(node, orm.InstalledCode) and not self.node.computer:
-                self.node.computer = node.computer
-
             # Need this special case for tests that use ProcessNodes as classes
             if isinstance(self.node, orm.CalculationNode):
                 self.node.base.links.add_incoming(node, LinkType.INPUT_CALC, name)
diff --git a/tests/engine/processes/calcjobs/test_calc_job.py b/tests/engine/processes/calcjobs/test_calc_job.py
index 85e96e83ee..d0e1c52763 100644
--- a/tests/engine/processes/calcjobs/test_calc_job.py
+++ b/tests/engine/processes/calcjobs/test_calc_job.py
@@ -874,11 +874,12 @@ class TestImport:
     """Test the functionality to import existing calculations completed outside of AiiDA."""
 
     @pytest.fixture(autouse=True)
-    def init_profile(self, aiida_profile_clean, aiida_localhost):  # pylint: disable=unused-argument
+    def init_profile(self, aiida_profile_clean, aiida_localhost, aiida_local_code_factory):  # pylint: disable=unused-argument
         """Initialize the profile."""
         # pylint: disable=attribute-defined-outside-init
         self.computer = aiida_localhost
         self.inputs = {
+            'code': aiida_local_code_factory('core.arithmetic.add', '/bin/bash', computer=aiida_localhost),
             'x': orm.Int(1),
             'y': orm.Int(2),
             'metadata': {