I sent an email to the settings and extensions teams, but for anyone else paying attention to this issue (and for future reference), work on this for policy/* and network/* is currently blocked on the following problem:

Some of our elements have extension API dependencies, specifically ones in policy/ (chrome.settingsPrivate) and network/ (chrome.networkingPrivate).

In cr_elements_browsertest.js we set, e.g., 
browsePreload: 'chrome://resources/cr_elements/policy/cr_policy_pref_indicator.html'.

This does not (as near as I can tell) cause chrome to load any extension APIs.

We can kind of work around this by adding, e.g. settings_private.js as an extra library:

  extraLibraries: CrElementsBrowserTest.prototype.extraLibraries.concat([
    '../../../../../third_party/closure_compiler/externs/settings_private.js',
    'cr_policy_pref_indicator_tests.js',
  ]),

However this winds up executing externs, which we don't want to do.

Does anyone have any thoughts on how to load e.g. settingsPrivate and networkingPrivate for chrome://resources/cr_elements/* (or perhaps for specific subdirs or files)? Or even loading all extension apis (slower presumably, but it's already a browser test).

The only alternative I can think of would be to modify the externs generator to generate a fake implementation with types just for tests, which would be kind of a heavyweight solution (but might simplify some of our existing fakes).

Would it be reasonable to always hide your usage of private extension APIs behind a "browser proxy"? Then you could create a TestBrowserProxy for your test and never have to load the real thing (there are already plenty examples of this, except that they wrap chrome.send calls, not extension API calls).

BTW here is an example of a browser proxy wrapping calls to private extension APIs, https://cs.chromium.org/chromium/src/chrome/browser/resources/settings/appearance_page/appearance_browser_proxy.js?l=45.

conversely, we could probably make a specific C++ test fixture that enables the extension APIs for these tests.

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/5f4f1ed5c5e0c32bda1b5da16f4f4dab37e276b8

commit 5f4f1ed5c5e0c32bda1b5da16f4f4dab37e276b8
Author: stevenjb <stevenjb@chromium.org>
Date: Fri Feb 17 06:34:18 2017

WebUI: Add cr-policy-pref-indicator tests

This adds some tests for cr-policy-pref-indicator.

It also fixes a potential issue if a pref property changes but not the entire pref.

BUG= 679561 
CQ_INCLUDE_TRYBOTS=master.tryserver.chromium.linux:closure_compilation

Review-Url: https://codereview.chromium.org/2624003003
Cr-Commit-Position: refs/heads/master@{#451248}

[modify] https://crrev.com/5f4f1ed5c5e0c32bda1b5da16f4f4dab37e276b8/chrome/test/data/webui/cr_elements/cr_elements_browsertest.js
[add] https://crrev.com/5f4f1ed5c5e0c32bda1b5da16f4f4dab37e276b8/chrome/test/data/webui/cr_elements/cr_policy_pref_indicator_tests.js
[modify] https://crrev.com/5f4f1ed5c5e0c32bda1b5da16f4f4dab37e276b8/ui/webui/resources/cr_elements/policy/cr_policy_indicator_behavior.js
[modify] https://crrev.com/5f4f1ed5c5e0c32bda1b5da16f4f4dab37e276b8/ui/webui/resources/cr_elements/policy/cr_policy_pref_behavior.js
[modify] https://crrev.com/5f4f1ed5c5e0c32bda1b5da16f4f4dab37e276b8/ui/webui/resources/cr_elements/policy/cr_policy_pref_indicator.html
[modify] https://crrev.com/5f4f1ed5c5e0c32bda1b5da16f4f4dab37e276b8/ui/webui/resources/cr_elements/policy/cr_policy_pref_indicator.js

FYI, https://codereview.chromium.org/2700063002 added some tests for cr-dialog.

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/0c3256d22e6966598c8d5cd101cd7e827b0f42b9

commit 0c3256d22e6966598c8d5cd101cd7e827b0f42b9
Author: stevenjb <stevenjb@chromium.org>
Date: Thu Mar 09 19:37:43 2017

WebUI: Add cr_policy_network_indicator_tests.js

This also makes indicatorType private for cr-policy-network-indicator
and switches existing usage to cr-policy-pref-indicator (which now
correctly supports indicator-type).

BUG= 679561 
CQ_INCLUDE_TRYBOTS=master.tryserver.chromium.linux:closure_compilation

Review-Url: https://codereview.chromium.org/2625213002
Cr-Commit-Position: refs/heads/master@{#455830}

[modify] https://crrev.com/0c3256d22e6966598c8d5cd101cd7e827b0f42b9/chrome/browser/resources/settings/internet_page/internet_detail_page.html
[modify] https://crrev.com/0c3256d22e6966598c8d5cd101cd7e827b0f42b9/chrome/test/data/webui/cr_elements/cr_elements_browsertest.js
[add] https://crrev.com/0c3256d22e6966598c8d5cd101cd7e827b0f42b9/chrome/test/data/webui/cr_elements/cr_policy_network_indicator_tests.js
[modify] https://crrev.com/0c3256d22e6966598c8d5cd101cd7e827b0f42b9/ui/webui/resources/cr_elements/network/cr_network_list_item.html
[modify] https://crrev.com/0c3256d22e6966598c8d5cd101cd7e827b0f42b9/ui/webui/resources/cr_elements/policy/cr_policy_network_indicator.js

Added tests for:
cr_dialog
cr_policy_network_indicator
cr_policy_pref_indicator

Tests also do exist for cr_search_field_behavior / cr_toolbar in cr_toolbar_search_field_tests.js.

cr_expand_button is a fairly trivial wrapper around paper-icon-button and should probably be replaced with some CSS eventually.

Created  issue 700121  to track testing for internet_page and cr_network_* tests.

closing it for now. please reopen if tests are not working as excepted.