How to properly redact a PDF
Redact a PDF properly with PDF by Zaweba: mark text, areas or pages, then Apply, which removes the text and picture pixels from the file itself.

Proper redaction takes two stages in PDF by Zaweba. First you mark what must go, by selecting text, drawing over an area or choosing whole pages. Then you Apply the redactions, and the text and picture pixels under the marks are removed from the file, not just covered. The app is free and works offline on Windows.
That second stage is what makes it proper. A black rectangle drawn over words hides them on screen, but the words are still in the file and can often be copied straight out.
Marking what to remove
Open the document and use the redaction tools in the Protect menu. Select text to mark words, draw a box to mark an area such as a signature, a photo or part of a table, or mark whole pages when nothing on them should be released.
For long documents, Find and mark finds words you type, and kinds of personal information by country: emails, payment card numbers (checked with the Luhn test), IBANs, dates, IP and web addresses, UK phone numbers, postcodes, National Insurance and NHS numbers, and US phone, Social Security and ZIP+4 numbers. It marks each one it finds for you to check.
Marks show where redaction will happen. Nothing is removed yet, so take your time and look through every page.
Choosing how redactions look
Before applying, choose the colour of the redaction boxes and any words to show over them. Black is traditional. Some organisations prefer white or grey, or words such as a reason code, so a reader knows something was withheld and why.
Applying the redactions
When you're sure, choose Apply. The text and the picture pixels under each mark are taken out of the file. Save the result as a new file and keep the unredacted original somewhere safe and separate, because Apply can't be undone in the saved copy.
Then check. Try selecting and copying where the redactions are. Search for a word you removed. Nothing should come back.
Things redaction doesn't cover on its own
Redaction removes what's under the marks on the page. A PDF can carry other things too: document details, XMP, attached files, comments, form fields, invisible text, content off the page, bookmarks, scripts, links and earlier versions. Protect, Remove hidden information lists them with counts so you can remove what's left, or Sanitise document removes all of it at once.
Earlier versions matter here. Ordinary saves are incremental, so an unredacted version may still sit inside the file. Removing hidden information or sanitising takes care of that.
If someone else has already blacked out a document, use Check for unsafe redactions. It finds boxes drawn over text that can still be copied, opaque comment boxes over text, and redaction marks never applied, and offers to mark them so Apply removes the text.
A safe routine
Mark, review, apply, remove hidden information, save as a new file, then test by copying and searching. PDF by Zaweba does every step on your own PC, which matters when the document is the sort that needed redacting in the first place.