Given:
$path = c:\dir1\dir2\dir3\dir4\dir5
I want to search for var.txt starting in the lowest child directory (dir5). 
If var.txt is there, do something, if not, search the next level (in this case dir4) for var.txt and repeat.  
Possibly relevant links:
How I could use test-path to check for var.txt
Ideas:
Somehow using Split-Path, in a loop which iterates -Parent, and using test-path each iteration to check for var.txt
Solution:
Incorporating the solution below with actions, and breaking the loop if not found at the highest directory:
$file = ""
$path = ""
while($path -and !(Test-Path (Join-Path $path $file))){
    if($path -eq ((Split-Path -Path $path -Qualifier)+"\")){
        break
    }
    else {
        $path = Split-Path $path -Parent
    }
}
if($path -ne ((Split-Path -Path $path -Qualifier)+"\")){
    #do something
}
 
     
    