Check for Matching Contacts no longer gives an option to merge
It looks like the merge link was taken away in a recent update when the page was updated to use ajax for the matching lookup.  For those who may be looking for a temporary work-around (until hopefully this comes back into the core product), using the URL info from @Demerit in the comments above, I looked for a way to add the Merge link back into the popup notification when a person clicks on the Find Matching Contacts button.  This can be done by creating a custom Contact.tpl template and modifying one line in the "duplicates-msg-tpl" section.

The way I did it was to override just that template section, and then re-import the main Contact.tpl file (since I don't want to have to manage merging things every time that template changes). Not sure why, but I had to use the full path for that include call. Here is the example custom Contact.tpl file (you need to first define where your custom templates go and include that in the Civi Admin system settings).  You may need to change the rgid to whatever rule id you use (it may not even be necessary to have that param in the URL at all, but I kept it there just in case).  You may also want to switch your cid and oid values, depending on which contact you want to merge into the other.  In this case, I'm assuming the one being edited should merge into the existing one that shows up on the list.

 {literal}
&lt;script type="text/template" id="duplicates-msg-tpl"&gt;
  &lt;em&gt;&lt;%- info %&gt;&lt;/em&gt;
  &lt;ul class="matching-contacts-actions"&gt;
    &lt;% _.forEach(contacts, function(contact) { %&gt;
      &lt;li&gt;
        &lt;a href="&lt;%= CRM.url('civicrm/contact/view', {reset: 1, cid: contact.id}) %&gt;"&gt;&lt;%- contact.display_name %&gt;&lt;/a&gt;{/literal}{if $contactId|intval &gt; 0}{literal} (&lt;a href="&lt;%= CRM.url('civicrm/contact/merge', {reset: 1, oid: {/literal}{$contactId|intval}{literal}, cid: contact.id, action: 'update', rgid: 4}) %&gt;"&gt;Merge&lt;/a&gt;){/literal}{/if}{literal}
        &lt;%- contact.email %&gt;
      &lt;/li&gt;
    &lt;% }); %&gt;
  &lt;/ul&gt;
&lt;/script&gt;
{/literal}
{include file="/var/www/civicrm/sites/all/modules/civicrm/templates/CRM/Contact/Form/Contact.tpl"}