diff --git a/tests/basics/sys_tracebacklimit.py.native.exp b/tests/basics/sys_tracebacklimit.py.native.exp
new file mode 100644
index 0000000000..f9d30c0585
--- /dev/null
+++ b/tests/basics/sys_tracebacklimit.py.native.exp
@@ -0,0 +1,22 @@
+ValueError: value
+
+limit 4
+ValueError: value
+
+limit 3
+ValueError: value
+
+limit 2
+ValueError: value
+
+limit 1
+ValueError: value
+
+limit 0
+ValueError: value
+
+limit -1
+ValueError: value
+
+True
+False
diff --git a/tests/micropython/emg_exc.py.native.exp b/tests/micropython/emg_exc.py.native.exp
new file mode 100644
index 0000000000..9677c526a9
--- /dev/null
+++ b/tests/micropython/emg_exc.py.native.exp
@@ -0,0 +1,2 @@
+ValueError: 1
+
diff --git a/tests/micropython/heapalloc_traceback.py.native.exp b/tests/micropython/heapalloc_traceback.py.native.exp
new file mode 100644
index 0000000000..d6ac26aa82
--- /dev/null
+++ b/tests/micropython/heapalloc_traceback.py.native.exp
@@ -0,0 +1,3 @@
+StopIteration
+StopIteration: 
+
diff --git a/tests/misc/print_exception.py.native.exp b/tests/misc/print_exception.py.native.exp
new file mode 100644
index 0000000000..59e856ae3c
--- /dev/null
+++ b/tests/misc/print_exception.py.native.exp
@@ -0,0 +1,18 @@
+caught
+Exception: msg
+
+caught
+Exception: fail
+
+finally
+caught
+Exception: fail
+
+reraise
+Exception: fail
+
+caught
+Exception: fail
+
+AttributeError: 'function' object has no attribute 'X'
+
diff --git a/tests/run-tests.py b/tests/run-tests.py
index f8174b2d3b..aeea0bad5e 100755
--- a/tests/run-tests.py
+++ b/tests/run-tests.py
@@ -126,12 +126,6 @@ emitter_tests_to_skip = {
         "basics/unboundlocal.py",
         # These require "raise from".
         "basics/exception_chain.py",
-        # These require proper traceback info.
-        "basics/sys_tracebacklimit.py",
-        "misc/print_exception.py",
-        "micropython/emg_exc.py",
-        "micropython/heapalloc_traceback.py",
-        "thread/thread_exc2.py",
         # These require stack-allocated slice optimisation.
         "micropython/heapalloc_slice.py",
         # These require running the scheduler.
diff --git a/tests/thread/thread_exc2.py.native.exp b/tests/thread/thread_exc2.py.native.exp
new file mode 100644
index 0000000000..9b2e715ef8
--- /dev/null
+++ b/tests/thread/thread_exc2.py.native.exp
@@ -0,0 +1,3 @@
+Unhandled exception in thread started by <function thread_entry at 0x\[0-9a-f\]\+>
+ValueError: 
+done