I will base my answer upon a statement from the OP's comments:
In a conference though, mentioning an affiliation which is not current would be a quite serious mistake.
As I have expressed before in another answer, I do not see any reason why an "affiliation" needs to be something explicitly formalized, or why affiliations need to be mutually exclusive.
As such, I disagree with the above statement.
At least in fields where the conference paper is an actual publication, and the presentation is simply a part of paper publication via the conference, basically, the author details (including affiliation) in the conference presentation on a paper should be the same as those indicated on the paper.
Some information can be added, though:
- The author who presents the paper in the conference may be highlighted.
- If someone other than one of the authors presents the paper, their name may be listed on the presentation (in such a way that it is clear they are the presenter and none of the authors).
- And, to address this question, if someone would like to update their contact or other details, they can indicate the changes during the presentation.
Lastly, for what it's worth, when you present a paper on a conference and that paper was created as a part of your work in your previous job, you are affiliated with that previous employer by the very act of presenting on behalf of your former position.
Therefore, I suggest the following course of action:
List your affiliation as it is stated on the paper.
Next to that, add something like "(now independent researcher)".