diff --git a/crates/environ/src/component/types.rs b/crates/environ/src/component/types.rs
index b6666308d4..4c715b61ef 100644
--- a/crates/environ/src/component/types.rs
+++ b/crates/environ/src/component/types.rs
@@ -469,6 +469,7 @@ impl ComponentTypesBuilder {
                 self.core_outer_type(0, TypeIndex::from_u32(*ty))
             }
             wasmparser::ComponentTypeRef::Func(ty)
+            | wasmparser::ComponentTypeRef::Type(_, ty)
             | wasmparser::ComponentTypeRef::Instance(ty)
             | wasmparser::ComponentTypeRef::Component(ty) => {
                 self.component_outer_type(0, ComponentTypeIndex::from_u32(*ty))
@@ -476,9 +477,6 @@ impl ComponentTypesBuilder {
             wasmparser::ComponentTypeRef::Value(..) => {
                 unimplemented!("references to value types");
             }
-            wasmparser::ComponentTypeRef::Type(..) => {
-                unimplemented!("references to types");
-            }
         }
     }
 
diff --git a/crates/wasmtime/src/component/matching.rs b/crates/wasmtime/src/component/matching.rs
index e5012a5043..ae38e3301a 100644
--- a/crates/wasmtime/src/component/matching.rs
+++ b/crates/wasmtime/src/component/matching.rs
@@ -72,6 +72,12 @@ impl TypeChecker<'_> {
         // the actual type. It's ok, though, to have extra exports in the actual
         // type.
         for (name, expected) in expected.exports.iter() {
+            // Interface types may be exported from a component in order to give them a name, but
+            // they don't have a definition in the sense that this search is interested in, so
+            // ignore them.
+            if let TypeDef::Interface(_) = expected {
+                continue;
+            }
             let actual = self
                 .strings
                 .lookup(name)
diff --git a/tests/misc_testsuite/component-model/instance.wast b/tests/misc_testsuite/component-model/instance.wast
index 74e5270122..d23fe605fa 100644
--- a/tests/misc_testsuite/component-model/instance.wast
+++ b/tests/misc_testsuite/component-model/instance.wast
@@ -179,6 +179,12 @@
   ))
 )
 
+(component
+  (import "host" (instance $i
+    (type $rec (record (field "x" (record)) (field "y" string)))
+    (export "some-record" (type (eq $rec)))))
+)
+
 (component
   (import "host" (instance $i
     (export "nested" (instance