Here is the way to do this:

1. Add client section to your karma.conf.js like this:

   plugins: [
       ...
   ],
   client: {
       codeCoverage: config.angularCli.codeCoverage
   },
   files: [
       ...
   ],
   

2. Change your test.ts to require files according to codeCoverage parameter:

   let context; 
   
   if (__karma__.config.codeCoverage) {
       context = require.context('./app/', true, /\.ts/);
   } else {
       context = require.context('./app/', true, /\.spec\.ts/);
   }
   
   context.keys().map(context);
   

UPDATE:

Since Angular CLI 1.5.0 additional steps are required:

3. Next to tsconfig.spec.json add tsconfig-cc.spec.json file with the following content:

   {
     "extends": "./tsconfig.spec.json",
     "include": [
       "**/*.ts"
     ]
   }
   

4. In your angular-cli.json add the following to apps array:

   {
     "root": "src/",
     "polyfills": "polyfills.ts",
     "test": "test.ts",
     "testTsconfig": "tsconfig-cc.spec.json"
   }
   

5. In your karma.conf.js add the following to angularCli section:

   app: config.angularCli.codeCoverage ? '1' : '0'  
   

   eventually it should look something like this:

   angularCli: {
       environment: 'dev',
       app: config.angularCli.codeCoverage ? '1' : '0'
   },
   

So what's happening here?

Apparently they have fixed Angular compiler plugin and it takes the file globs from tsconfig.spec.json now. As long as we include only **/*.spec.ts in tsconfig.spec.json these are the only files that will be included in coverage.

The obvious solution is making tsconfig.spec.json include all the files (in addition to require.context). However, this will slow down all the tests even when running without coverage (which we don't want to).

One of the solutions is using the ability of angular-cli to work with multiple apps.
By adding another entry into apps array, we're adding another configuration for "another" (which is actually the same one) app.
We strip out all the irrelevant information in this config, leaving just the test configuration, and put another tsconfig which includes all the ts files.
Finally, we're telling angular-cli karma plugin to run the tests with the configuration of the second app (index 1) in case it is running with code coverage and run with the configuration of the first app (index 0) if it is running without code coverage.

Important note: in this configuration I assume you have only one application in .angular-cli.json. In case you have more you have to adjust indexes accordingly.

Solution provided by Narm is really great, however still not ideal, as requires importing manually at least all the lazy loaded modules + root one to the tests and also on big projects there are almost always some non-used/forgotten components which are not part of any production code and which will leave in the source code for ever untested/undiscovered.

Solution:

https://github.com/kopach/karma-sabarivka-reporter.

To use it → install npm install --save-dev karma-sabarivka-reporter

And update karma.conf.js as described here https://github.com/kopach/karma-sabarivka-reporter#-usage

After this – all files matching pattern will be included into final coverage result

As @Chellappan pointed out, the framework was including a library in the code coverage. Because it was referenced in one of my components. I was able to exclude it from code coverage through the following in angular-cli.json

"test": {
    "codeCoverage": {
      "exclude": [
        "src/assets/jqwidgets/**/*",
        "src/assets/jqwidgets-ts/**/*"
      ]
    },

First install the dependencies.

npm install karma karma-jasmine karma-chrome-launcher karma-jasmine-html-reporter karma-coverage-istanbul-reporter

Then run ng test.

ng test --code-coverage

Then run the server that shows you your report.

http-server -c-1 -o -p 9875 ./coverage

You should see something like this:

I wrote a blog post about this here.