diff --git a/docs/examples/tutorials/tuning-a-process.md b/docs/examples/tutorials/tuning-a-process.md
index 071f76d9..4c8d3651 100644
--- a/docs/examples/tutorials/tuning-a-process.md
+++ b/docs/examples/tutorials/tuning-a-process.md
@@ -58,6 +58,9 @@ Running this code will execute an optimisation job and print out information on
 !!! tip
     Since [Optuna](https://optuna.org/) is used under the hood, you can configure the optional `algorithm` argument on the `Tuner` with additional configuration defined in [`OptunaSpec`][plugboard.schemas.OptunaSpec]. For example, the [`storage`](https://optuna.readthedocs.io/en/stable/reference/storages.html) argument allows you to save the optimisation results to a database or SQLite file. You can then use a tool like [Optuna Dashboard](https://optuna-dashboard.readthedocs.io/en/stable/getting-started.html) to study the optimisation output in more detail.
 
+!!! tip
+    You can impose arbitary constraints on variables within a `Process`. In your `step` method you can raise a [`ConstraintError`][plugboard.exceptions.ConstraintError] to indicate to the `Tuner` that a constraint has been breached. This will cause the trial to be stopped, and the optimisation will continue trying to find parameters that don't cause the constraint violation.
+
 ## Using YAML config
 
 Plugboard's YAML config supports an optional `tune` section, allowing you to define optimisation jobs alongside your model configuration:
diff --git a/plugboard/exceptions/__init__.py b/plugboard/exceptions/__init__.py
index 75fccd74..5dd488da 100644
--- a/plugboard/exceptions/__init__.py
+++ b/plugboard/exceptions/__init__.py
@@ -89,3 +89,9 @@ class ValidationError(Exception):
     """Raised when an invalid `Process` or `Component` is encountered."""
 
     pass
+
+
+class ConstraintError(Exception):
+    """Raised when a constraint is violated."""
+
+    pass
diff --git a/plugboard/tune/tune.py b/plugboard/tune/tune.py
index 6e0fd090..aa678fc4 100644
--- a/plugboard/tune/tune.py
+++ b/plugboard/tune/tune.py
@@ -1,12 +1,14 @@
 """Provides `Tuner` class for optimising Plugboard processes."""
 
 from inspect import isfunction
+import math
 from pydoc import locate
 import typing as _t
 
 import ray.tune.search.optuna
 
 from plugboard.component.component import Component, ComponentRegistry
+from plugboard.exceptions import ConstraintError
 from plugboard.process import Process, ProcessBuilder
 from plugboard.schemas import (
     Direction,
@@ -52,6 +54,8 @@ def __init__(
             algorithm: Configuration for the underlying Optuna algorithm used for optimisation.
         """
         self._logger = DI.logger.resolve_sync().bind(cls=self.__class__.__name__)
+        # Check that objective and mode are lists of the same length if multiple objectives are used
+        self._check_objective(objective, mode)
         self._objective = objective if isinstance(objective, list) else [objective]
         self._mode = [str(m) for m in mode] if isinstance(mode, list) else str(mode)
         self._metric = (
@@ -79,6 +83,22 @@ def result_grid(self) -> ray.tune.ResultGrid:
             raise ValueError("No result grid available. Run the optimisation job first.")
         return self._result_grid
 
+    @classmethod
+    def _check_objective(
+        cls, objective: ObjectiveSpec | list[ObjectiveSpec], mode: Direction | list[Direction]
+    ) -> None:
+        """Check that the objective and mode are valid."""
+        if isinstance(objective, list):
+            if not isinstance(mode, list):
+                raise ValueError("If using multiple objectives, `mode` must also be a list.")
+            if len(objective) != len(mode):
+                raise ValueError(
+                    "If using multiple objectives, `mode` and `objective` must be the same length."
+                )
+        else:
+            if isinstance(mode, list):
+                raise ValueError("If using a single objective, `mode` must not be a list.")
+
     def _build_algorithm(
         self, algorithm: _t.Optional[OptunaSpec] = None
     ) -> ray.tune.search.Searcher:
@@ -189,7 +209,7 @@ def run(self, spec: ProcessSpec) -> ray.tune.Result | list[ray.tune.Result]:
     def _build_objective(
         self, component_classes: dict[str, type[Component]], spec: ProcessSpec
     ) -> _t.Callable:
-        def fn(config: dict[str, _t.Any]) -> _t.Any:  # pragma: no-cover
+        def fn(config: dict[str, _t.Any]) -> dict[str, _t.Any]:  # pragma: no cover
             # Recreate the ComponentRegistry in the Ray worker
             for key, cls in component_classes.items():
                 ComponentRegistry.add(cls, key=key)
@@ -198,8 +218,23 @@ def fn(config: dict[str, _t.Any]) -> _t.Any:  # pragma: no-cover
                 self._override_parameter(spec, self._parameters_dict[name], value)
 
             process = ProcessBuilder.build(spec)
-            run_coro_sync(self._run_process(process))
-
-            return {obj.full_name: self._get_objective(process, obj) for obj in self._objective}
+            result = {}
+            try:
+                run_coro_sync(self._run_process(process))
+                result = {
+                    obj.full_name: self._get_objective(process, obj) for obj in self._objective
+                }
+            except* ConstraintError as e:
+                modes = self._mode if isinstance(self._mode, list) else [self._mode]
+                self._logger.warning(
+                    "Constraint violated during optimisation, stopping early",
+                    constraint_error=str(e),
+                )
+                result = {
+                    obj.full_name: math.inf if mode == "min" else -math.inf
+                    for obj, mode in zip(self._objective, modes)
+                }
+
+            return result
 
         return fn
diff --git a/tests/integration/test_tuner.py b/tests/integration/test_tuner.py
index e3f997a4..4e35b645 100644
--- a/tests/integration/test_tuner.py
+++ b/tests/integration/test_tuner.py
@@ -1,14 +1,27 @@
 """Integration tests for the `Tuner` class."""
 
+import math
+
 import msgspec
 import pytest
 
+from plugboard.exceptions import ConstraintError
 from plugboard.schemas import ConfigSpec, ConnectorBuilderSpec, ObjectiveSpec
 from plugboard.schemas.tune import CategoricalParameterSpec, IntParameterSpec, OptunaSpec
 from plugboard.tune import Tuner
 from tests.integration.test_process_with_components_run import A, B, C  # noqa: F401
 
 
+class ConstrainedB(B):
+    """Component with a constraint."""
+
+    async def step(self) -> None:
+        """Override step to apply a constraint."""
+        if self.in_1 > 10:
+            raise ConstraintError("Input must not be greater than 10")
+        await super().step()
+
+
 @pytest.fixture
 def config() -> dict:
     """Loads the YAML config."""
@@ -59,10 +72,10 @@ async def test_tune(config: dict, mode: str, process_type: str, ray_ctx: None) -
     assert not [t for t in result if t.error]
     # Correct optimimum must be found (within tolerance)
     if mode == "min":
-        assert best_result.config["a.iters"] <= tuner._parameters["a.iters"].lower + 1
+        assert best_result.config["a.iters"] <= tuner._parameters["a.iters"].lower + 2
         assert best_result.metrics["c.in_1"] == best_result.config["a.iters"] - 1
     else:
-        assert best_result.config["a.iters"] >= tuner._parameters["a.iters"].upper - 1
+        assert best_result.config["a.iters"] >= tuner._parameters["a.iters"].upper - 2
         assert best_result.metrics["c.in_1"] == best_result.config["a.iters"] - 1
 
 
@@ -121,3 +134,47 @@ async def test_multi_objective_tune(config: dict, ray_ctx: None) -> None:
     assert -1 in set(r.config["b.factor"] for r in best_result)
     assert -1 in set(r.metrics["b.out_1"] for r in best_result)
     assert 1 in set(r.metrics["c.in_1"] for r in best_result)
+
+
+@pytest.mark.tuner
+@pytest.mark.asyncio
+async def test_tune_with_constraint(config: dict, ray_ctx: None) -> None:
+    """Tests running of optimisation jobs with a constraint."""
+    spec = ConfigSpec.model_validate(config)
+    process_spec = spec.plugboard.process
+    # Replace component B with a constrained version
+    process_spec.args.components[1].type = "tests.integration.test_tuner.ConstrainedB"
+    tuner = Tuner(
+        objective=ObjectiveSpec(
+            object_type="component",
+            object_name="c",
+            field_type="field",
+            field_name="in_1",
+        ),
+        parameters=[
+            IntParameterSpec(
+                object_type="component",
+                object_name="a",
+                field_type="arg",
+                field_name="iters",
+                lower=5,
+                upper=15,
+            )
+        ],
+        num_samples=12,
+        mode="max",
+        max_concurrent=2,
+        algorithm=OptunaSpec(),
+    )
+    best_result = tuner.run(
+        spec=process_spec,
+    )
+    result = tuner.result_grid
+    # There must be no failed trials
+    assert not [t for t in result if t.error]
+    # Constraint must be respected
+    assert all(t.metrics["c.in_1"] <= 10 for t in result)
+    # Optimum must be less than or equal to 10
+    assert best_result.metrics["c.in_1"] <= 10
+    # If a.iters is greater than 11, the constraint will be violated
+    assert all(t.metrics["c.in_1"] == -math.inf for t in result if t.config["a.iters"] > 11)