diff --git a/lib/query_processing/src/expressions.rs b/lib/query_processing/src/expressions.rs
index 14dc0ea4..a39839f1 100644
--- a/lib/query_processing/src/expressions.rs
+++ b/lib/query_processing/src/expressions.rs
@@ -190,10 +190,19 @@ pub fn variable(
     context: &Context,
 ) -> Result<SolutionMappings, QueryProcessingError> {
     if !solution_mappings.rdf_node_types.contains_key(v.as_str()) {
-        return Err(QueryProcessingError::VariableNotFound(
-            v.as_str().to_string(),
+        // A variable that does not occur in the pattern is unbound in every solution
+        // (SPARQL 1.1, section 18.6), e.g. ORDER BY ?x or COALESCE(?x, ...) where ?x is
+        // never bound. Evaluate it as unbound instead of failing the query.
+        solution_mappings.mappings = solution_mappings.mappings.with_column(
+            lit(LiteralValue::untyped_null())
+                .cast(BaseRDFNodeType::None.default_input_polars_data_type())
+                .alias(context.as_str()),
+        );
+        solution_mappings.rdf_node_types.insert(
             context.as_str().to_string(),
-        ));
+            BaseRDFNodeType::None.into_default_input_rdf_node_state(),
+        );
+        return Ok(solution_mappings);
     }
     solution_mappings.mappings = solution_mappings
         .mappings
@@ -427,10 +436,15 @@ pub fn bound(
     outer_context: &Context,
 ) -> Result<SolutionMappings, QueryProcessingError> {
     if !solution_mappings.rdf_node_types.contains_key(v.as_str()) {
-        return Err(QueryProcessingError::VariableNotFound(
-            v.as_str().to_string(),
+        // A variable that does not occur in the pattern is never bound.
+        solution_mappings.mappings = solution_mappings
+            .mappings
+            .with_column(lit(false).alias(outer_context.as_str()));
+        solution_mappings.rdf_node_types.insert(
             outer_context.as_str().to_string(),
-        ));
+            BaseRDFNodeType::Literal(xsd::BOOLEAN.into_owned()).into_default_input_rdf_node_state(),
+        );
+        return Ok(solution_mappings);
     }
     let expr = expr_is_null_workaround(
         col(v.as_str()),
diff --git a/py_maplib/tests/test_unbound_variables.py b/py_maplib/tests/test_unbound_variables.py
new file mode 100644
index 00000000..8e7fe95d
--- /dev/null
+++ b/py_maplib/tests/test_unbound_variables.py
@@ -0,0 +1,57 @@
+import pytest
+
+from maplib import Model
+
+# SPARQL 1.1 18.6: a variable that does not occur in the pattern is unbound in every
+# solution. Expressions that use it must evaluate as with any other unbound variable
+# instead of failing the query.
+
+
+@pytest.fixture
+def model():
+    m = Model()
+    m.reads(
+        '<http://example.net/a> <http://example.net/p> "b" .\n'
+        '<http://example.net/b> <http://example.net/p> "a" .\n',
+        format="ntriples",
+    )
+    return m
+
+
+def test_order_by_variable_not_in_pattern(model):
+    df = model.query(
+        "SELECT ?s WHERE { ?s <http://example.net/p> ?o } ORDER BY ?nope ?o"
+    )
+    assert df["s"].to_list() == ["<http://example.net/b>", "<http://example.net/a>"]
+
+
+def test_distinct_order_by_variable_not_in_pattern(model):
+    df = model.query(
+        "SELECT DISTINCT ?s WHERE { ?s <http://example.net/p> ?o } ORDER BY ?nope"
+    )
+    assert sorted(df["s"].to_list()) == [
+        "<http://example.net/a>",
+        "<http://example.net/b>",
+    ]
+
+
+def test_bound_variable_not_in_pattern(model):
+    df = model.query(
+        "SELECT ?s WHERE { ?s <http://example.net/p> ?o FILTER(!BOUND(?nope)) }"
+    )
+    assert df.height == 2
+
+
+def test_coalesce_variable_not_in_pattern(model):
+    df = model.query(
+        "SELECT ?s ?x WHERE { ?s <http://example.net/p> ?o "
+        "BIND(COALESCE(?nope, ?o) AS ?x) } ORDER BY ?x"
+    )
+    assert df["x"].to_list() == ["a", "b"]
+
+
+def test_filter_on_variable_not_in_pattern(model):
+    df = model.query(
+        'SELECT ?s WHERE { ?s <http://example.net/p> ?o FILTER(?nope = "a") }'
+    )
+    assert df.height == 0