I have a portal within my main layout that I use for all phone log comments and documents.

Is there an example or a (best practice) way to create a search field that searches within that portal only and shows the correct records searched?

You could use a search button to perform a script.  That script could open a small card window, or use Input fields in Show custom dialog.  

But what do you want to do after the search?  All of this can be scripted.

Keep in mind if you search in a portal, you get all the parent records that have a portal record that contain that value.  As an example, if you're searching for yesterday's date in a portal, you don't get just portal records with yesterday's date.  You get all the parent records that have a portal record with yesterday's date.  So as you flip through the parent records, you'll see portal records with all records related to each parent record.

You could use a portal filter to just show the portal records of the searched 'date'.  But you would also have to clear that filter to avoid user confusion.

Now if you just want to show only the portal records that match the search criteria, you may be better off going to a layout based on the portal, maybe even in a new window, where you can flip through the records, then close the window.  This way you wouldn't disturb your first window's found set.