Seeking Courts-Martial transcripts

According to The Guide to Federal Records, court martial records are spread across several record group depending on the branch of the service and also in the AGO.  https://search.archives.gov/search/docs?utf8=&affiliate=national-archives&query=court+martial&dc=3518

Doing a very quick search on www.Fold3.com, I found a fair number of Navy cases (most had quite a few pages) and a large number of WWI Army cases (I realize too recent for your research).  There may be others if one searches with a name or other details (I was just using "court martial").

Without knowing which branch of service you are referencing and what you've already found, it is impossible to provide any meaningful response. Please link what you already found on the website and explain what you are trying to research in greater detail.

According to the links you provided, these records are available at the National Archives (NARA) in Washington DC. 

Dear Mr. Webster,

Thank you for posting your request on History Hub!

These files are part of the record series Court Martial Case Files, 12/1800 - 10/1894 in the Records of the Office of the Judge Advocate General (Army) (Record Group 153). This series has not been digitized or indexed at the individual document level, and it is likely that the exact file contents vary from case to case.  However, according to the Scope and Content Note in the series level catalog description, this series includes are documents describing the organization and personnel of the courts; charges and specifications; pleas and arraignments of the defendants; papers and exhibits submitted for the consideration of the courts; proceedings, findings, and sentences of the courts; reports of the reviewing authorities; statements of action by the Secretary of War and the President of the United States; and related correspondence and evidence.  Therefore, it is likely that the files include at a minimum the charges and outcome, and they may contain additional details. The series description does not specifically address transcripts. For more information about these records, please contact the National Archives at Washington, DC - Textual Reference (RDT1) via email at Archives1reference@nara.gov.

Due to the COVID-19 pandemic and pursuant to guidance received from the Office of Management and Budget (OMB), NARA has adjusted its normal operations to balance the need of completing its mission-critical work while also adhering to the recommended social distancing for the safety of NARA staff. As a result of this re-prioritization of activities, you may experience a delay in receiving an initial acknowledgement as well as a substantive response to your reference request from RDT1. We apologize for this inconvenience and appreciate your understanding and patience.

We hope this is helpful. Best of luck with your research!