You can search for transactions by Credit Card by using the report "Credit Card Processing Details". The minimum amount of information you will need is the last 4 digits of the Credit Card number. The more information you have about the transaction, the easier it will be to determine the exact transaction.
1) Navigate to Reports and find the Credit Card Processing Details report.
2) Fill in the report filters to search for the specific transaction.
3) Click on the search button.
If you are not finding the transaction and you are specifying a date range, try expanding the date range by a few weeks.
Keep in mind, you can add/remove columns. If you needed the transaction number you can click the [+] sign and select Trans. # from the list to add the column. Below is a video showing how to find and use the Credit Card Processing Details report: