diff --git a/datasette/app.py b/datasette/app.py
index aa75d772a3..23d21600c6 100644
--- a/datasette/app.py
+++ b/datasette/app.py
@@ -930,7 +930,7 @@ async def permission_allowed(
             used_default = True
         self._permission_checks.append(
             {
-                "when": datetime.datetime.utcnow().isoformat(),
+                "when": datetime.datetime.now(datetime.timezone.utc).isoformat(),
                 "actor": actor,
                 "action": action,
                 "resource": resource,
diff --git a/datasette/default_magic_parameters.py b/datasette/default_magic_parameters.py
index 1938220765..91c1c5aa0a 100644
--- a/datasette/default_magic_parameters.py
+++ b/datasette/default_magic_parameters.py
@@ -24,9 +24,12 @@ def now(key, request):
     if key == "epoch":
         return int(time.time())
     elif key == "date_utc":
-        return datetime.datetime.utcnow().date().isoformat()
+        return datetime.datetime.now(datetime.timezone.utc).date().isoformat()
     elif key == "datetime_utc":
-        return datetime.datetime.utcnow().strftime(r"%Y-%m-%dT%H:%M:%S") + "Z"
+        return (
+            datetime.datetime.now(datetime.timezone.utc).strftime(r"%Y-%m-%dT%H:%M:%S")
+            + "Z"
+        )
     else:
         raise KeyError