diff --git a/integration_tests/__tests__/to_throw_error_matching_snapshot.test.js b/integration_tests/__tests__/to_throw_error_matching_snapshot.test.js
index 78ad60584084..e304b3a2cd16 100644
--- a/integration_tests/__tests__/to_throw_error_matching_snapshot.test.js
+++ b/integration_tests/__tests__/to_throw_error_matching_snapshot.test.js
@@ -48,19 +48,19 @@ test(`throws the error if tested function didn't throw error`, () => {
   }
 });
 
-test('does not accept arguments', () => {
-  const filename = 'does-not-accept-arguments.test.js';
-  const template = makeTemplate(`test('does not accept arguments', () => {
+test('accepts custom snapshot name', () => {
+  const filename = 'accept-custom-snapshot-name.test.js';
+  const template = makeTemplate(`test('accepts custom snapshot name', () => {
       expect(() => { throw new Error('apple'); })
-        .toThrowErrorMatchingSnapshot('foobar');
+        .toThrowErrorMatchingSnapshot('custom-name');
     });
     `);
 
   {
     writeFiles(TESTS_DIR, {[filename]: template()});
     const {stderr, status} = runJest(DIR, ['-w=1', '--ci=false', filename]);
-    expect(stderr).toMatch('Matcher does not accept any arguments.');
-    expect(status).toBe(1);
+    expect(stderr).toMatch('1 snapshot written in 1 test suite.');
+    expect(status).toBe(0);
   }
 });
 
diff --git a/packages/jest-snapshot/src/index.js b/packages/jest-snapshot/src/index.js
index bd59c992baa5..69c9ead962b6 100644
--- a/packages/jest-snapshot/src/index.js
+++ b/packages/jest-snapshot/src/index.js
@@ -14,12 +14,7 @@ import type {Path, SnapshotUpdateState} from 'types/Config';
 import fs from 'fs';
 import path from 'path';
 import diff from 'jest-diff';
-import {
-  EXPECTED_COLOR,
-  ensureNoExpected,
-  matcherHint,
-  RECEIVED_COLOR,
-} from 'jest-matcher-utils';
+import {EXPECTED_COLOR, matcherHint, RECEIVED_COLOR} from 'jest-matcher-utils';
 import SnapshotState from './State';
 import {addSerializer, getSerializers} from './plugins';
 import * as utils from './utils';
@@ -67,7 +62,9 @@ const toMatchSnapshot = function(received: any, testName?: string) {
   }
 
   const result = snapshotState.match(
-    testName || currentTestName || '',
+    testName && currentTestName
+      ? `${currentTestName}: ${testName}`
+      : currentTestName || '',
     received,
   );
   const {count, pass} = result;
@@ -115,7 +112,10 @@ const toMatchSnapshot = function(received: any, testName?: string) {
   };
 };
 
-const toThrowErrorMatchingSnapshot = function(received: any, expected: void) {
+const toThrowErrorMatchingSnapshot = function(
+  received: any,
+  testName?: string,
+) {
   this.dontThrow && this.dontThrow();
   const {isNot} = this;
 
@@ -125,8 +125,6 @@ const toThrowErrorMatchingSnapshot = function(received: any, expected: void) {
     );
   }
 
-  ensureNoExpected(expected, '.toThrowErrorMatchingSnapshot');
-
   let error;
 
   try {
@@ -144,7 +142,7 @@ const toThrowErrorMatchingSnapshot = function(received: any, expected: void) {
     );
   }
 
-  return toMatchSnapshot.call(this, error.message);
+  return toMatchSnapshot.call(this, error.message, testName);
 };
 
 module.exports = {