diff --git a/toolchain/check/cpp/type_mapping.cpp b/toolchain/check/cpp/type_mapping.cpp
index 6b5da01ab821..49fbedbec808 100644
--- a/toolchain/check/cpp/type_mapping.cpp
+++ b/toolchain/check/cpp/type_mapping.cpp
@@ -110,22 +110,26 @@ static auto TryMapClassType(Context& context, SemIR::ClassType class_type)
       break;
     }
     case SemIR::TypeLiteralInfo::Numeric: {
+      // Carbon supports large bit width beyond C++ builtins; we don't need to
+      // translate those.
+      if (!literal.numeric.bit_width_id.is_embedded_value()) {
+        return clang::QualType();
+      }
+      int bit_width = literal.numeric.bit_width_id.AsValue();
+
       switch (literal.numeric.kind) {
         case SemIR::NumericTypeLiteralInfo::None: {
           CARBON_FATAL("Unexpected invalid numeric type literal");
         }
         case SemIR::NumericTypeLiteralInfo::Float: {
           return context.ast_context().getRealTypeForBitwidth(
-              literal.numeric.bit_width_id.AsValue(),
-              clang::FloatModeKind::NoFloat);
+              bit_width, clang::FloatModeKind::NoFloat);
         }
         case SemIR::NumericTypeLiteralInfo::Int: {
-          return context.ast_context().getIntTypeForBitwidth(
-              literal.numeric.bit_width_id.AsValue(), true);
+          return context.ast_context().getIntTypeForBitwidth(bit_width, true);
         }
         case SemIR::NumericTypeLiteralInfo::UInt: {
-          return context.ast_context().getIntTypeForBitwidth(
-              literal.numeric.bit_width_id.AsValue(), false);
+          return context.ast_context().getIntTypeForBitwidth(bit_width, false);
         }
       }
     }
diff --git a/toolchain/check/testdata/interop/cpp/function/param_unsupported.carbon b/toolchain/check/testdata/interop/cpp/function/param_unsupported.carbon
index 134dfc9568ea..57a22a81a2a1 100644
--- a/toolchain/check/testdata/interop/cpp/function/param_unsupported.carbon
+++ b/toolchain/check/testdata/interop/cpp/function/param_unsupported.carbon
@@ -58,6 +58,44 @@ fn F() {
   //@dump-sem-ir-end
 }
 
+// ============================================================================
+// Unconvertible integer argument.
+// ============================================================================
+
+// --- int_param.h
+
+auto foo(int a) -> void;
+
+// --- fail_large_int.carbon
+
+library "[[@TEST_NAME]]";
+
+import Cpp library "int_param.h";
+
+// This doesn't have a direct type mapping in `getIntTypeForBitwidth`.
+fn F(x: i512) {
+  // CHECK:STDERR: fail_large_int.carbon:[[@LINE+4]]:11: error: call argument of type `i512` is not supported [CppCallArgTypeNotSupported]
+  // CHECK:STDERR:   Cpp.foo(x);
+  // CHECK:STDERR:           ^
+  // CHECK:STDERR:
+  Cpp.foo(x);
+}
+
+// --- fail_very_large_int.carbon
+
+library "[[@TEST_NAME]]";
+
+import Cpp library "int_param.h";
+
+// This doesn't fit as an embedded `IntId` value.
+fn F(x: i8388608) {
+  // CHECK:STDERR: fail_very_large_int.carbon:[[@LINE+4]]:11: error: call argument of type `i8388608` is not supported [CppCallArgTypeNotSupported]
+  // CHECK:STDERR:   Cpp.foo(x);
+  // CHECK:STDERR:           ^
+  // CHECK:STDERR:
+  Cpp.foo(x);
+}
+
 // CHECK:STDOUT: --- fail_todo_import_unsupported_primitive_type.carbon
 // CHECK:STDOUT:
 // CHECK:STDOUT: constants {