The project has no clear license file
If the project does not have a file that clearly spells out under which terms the project can be used, then you must assume that the default copyright protection applies. This means that only the author of the code is allowed to make copies, make changes or do anything useful with the code. In short, you can't use it.
If the code is in a public repository and there are statements from the owner of the repository indicating that the code is intended to be open-source, you can inform the owner that the license and/or copyright status is unclear and that it can't be considered open-source until that has been resolved.
The project does have a clear license, but no clear copyright information
This situation is somewhat unusual, but it can happen.
First of all, the license file typically does not contain copyright information. The license itself wasn't written by the author of the code (I would hope), so he can't put his copyright on it, and for all the major licenses it is accepted practice that they are used without a copyright statement of the license author.
If, at first glance, there is no copyright statement in sight, I would first double-check all the files in the repository, starting with the source files and excluding the files that appear to be third-party dependencies that were copied. Source files are the most likely files to contain a copyright statement.
If there really is no copyright statement in any of the files (excluding third-party dependencies), then it is time to file a bug report against the repository asking the owner to clear up the copyright status.
In the mean time, if the repository has a public record of the changes that were made (or the pull requests that were merged), you can assume that the copyright is shared between all the persons that have contributed to the project. If the project has more than a handful contributors and you need the information just for a proper acknowledgement in your project, I doubt that anyone has a problem with an acknowledgement in the form of "the contributors of ".