You can encourage users (mainly new users not familliar with the SE system) to accept. If you see one of your/somebody else's answer which should, in your opinion, be accepted, you can leave a comment as so to encourage the OP to accept the answer by giving them a gentle nudge:
@userXYZ If this answer solved your problem, then feel free to click that checkmark to the left of the answer. That will let others know that your problem was solved, which makes it easier for future visitors with the same problem to find a solution.
Or perhaps a shorter:
@userXYZ As a bonus, if this answer helped you, don't forget to click the gray checkmark next to the answer! Thanks!
If the OP provides feedback by accepting, or explaining why not to accept, you can leave a
@userXYZ Thanks for coming back and helping future visitors by accepting this post!
@userXYZ Thanks for coming back and providing feedback to help us resolve the problem!
On the other hand, if the user ignores your comment (eg. visits this site and doesn't respond), just delete and repost it.
Once the issue has been solved, wait a while, then delete your comments and flag the OP's as