1. Add a check before running the code, something like
If IsNull(FieldName) or FieldName="" Then Exit Sub

2. What is the code for this button? Is it trying to open it based on the name instead of the ID?

1.  thank you Adam for getting back to me so promptly.  I inserted your line of code at the top, and it stopped the error message. And then it simply exits the search, as instructed.  Is there a way to modify this so that it does not exit, and then simply lets me enter a search term, even though the field I click on is blank? as long as the filed has text in it, it executes the search perfectly. Of course I should aspire not to have blank fields in this column but every now and then I  do and would like to search my way out of one...  

Here's the whole Code statement, WITHOUT your addition:

Private Sub SearchProjectBtn_Click()
    
    Dim S As String
    S = InputBox("Enter Project", "Project", Project)
    If S = "" Then Exit Sub
    Me.Filter = "Project LIKE ""*" & S & "*"""
    Me.FilterOn = True
    
End Sub

2.  re: the Apostrophe problem:  I'm using an "OpenForm on click" button.

the WHERE CONDITION = is this:
="[Project]=" & "'" & [ProjectName] & "'"

1. I don't think I understand what your saying. Why would you click the search button to search what is in the field if there was nothing in the field? Or are you wanting a way to search for records with no data in the field, and to use an empty search text box + the button to do that?

2. I'm not used to macros so change it to VBA, delete the macro and select code editor instead.
DoCmd.OpenForm "FormName",,,"Project=""" & [ProjectName] & """"

Re: point #1. Sorry, I may not be using precise terminology, still being somewhat new to this.  ( I am systematically going through Richard's beginner course, but every now and then jump to one of his YouTube's for a specific thing - such as the search button-- that I haven't encountered yet in my courses.)  
So, no, I am not searching for No-Data fields, and I am not trying to search within the blank field itself.  my intention, at least, was to search THAT FIELD across the WHOLE TABLE and find a match for what I put in the text box that pops up when I click the search button.

so basically, I have a continuous form that lists all my Projects by name only.  I installed the search button next to the ProjectName field in my continuous form, with the intention of its being able to search the whole Project Table, as a way of helping me jump quickly to a particular record -- i.e. a record where the field name matches what I put in the box that pops up when I click on the search button.   [Perhaps I should have simply put it in the header of my Project list form, rather than next to every single item in the list?]  

There are always a few fields where the ProjectName is blank, usually through an error or incomplete entry in the table.  I've been reluctant to simply delete them until I get to explore the Table itself.  But the blanks happen to sort to the top of my continuous form, so I end up wanting to click my search button when it is next to one of the blank ProjectName fields, so I can find the record I am looking for. If I do that from the Button next to a blank field, I get rebuked by the error message.  But if I click the Button when it's next to a field with data, it opens a box, allows me to enter the name of the record I'm looking for, and it takes me right to it.  

I can easily work around this, either by scrolling to a field with data, or by entering token data, such as an X in the blank field name.  And your fix (thank you) at least makes the Rebuke message go away.  But it just bugs me that I'm not getting it to work the way I want!

The simple solution is to not allow project names to have ' in them. Just look at most airlines. When you book a flight, they don't allow ' in last names. My fiance's name is "D'Angelo" and it's ALWAYS a problem. LOL

sorry I think I'm using "field name" improperly.  what I mean  is the TEXT ENTRY in that particular field.  so for example, I'm next to a ProjectName that happens to be blank, and I want to find a Project named "Jones Appeal".  My intention was that I could simply click on that Search Button, enter "Jones Appeal" in the search's text box, and the form would jump to the Project named Jones Appeal (there are a few hundred projects in the list, so that's a lot quicker than scrolling).  Hopefully that's clear?! thanks again for your guidance.

thanks for your comment Richard, I guess I could go that route (banishing apostrophe's) without too much difficulty.  But here's why I didn't think I had to settle for that:  The Search button (though it's causing me the other minor problem #1 I'm discussing above) doesn't have any trouble with apostrophe's.  It's only the "Open Project" button that balks at them (problem #2).  Maybe it's because I'm using LIKE for the Search Button, but that's not an option with the Open Project button? (Since I want it to open the exact project named in the field?) Perhaps the LIKE allows it to ignore the objectionable apostrophe?