Depends on the county. Clerks throughout Montana have sites which will tell you how and where to get the marriage record. Unless you'd like to get a private company to do it for you.
Persons and businesses don't get the same protections form privacy laws which limit open records. Public records generally apply to public entities and their duty to be transparent and provide information/records when in their custody. In some cases when a private company is working on the behalf of a government agency, they will be under similar laws. However, private entities don't get the same privacy protections.
There were 10438 divorces filed in Montana's district courts, listed under domestic relations filings. There are breakdowns of statistics by individual district courts open to the public from the state court's site. The statistics go back to 2001 for all case filings and dispositions in district courts.
In 2014, the Montana district court issued 3519 subpoenas and search warrants. The state's most populated county, Yellowstone in the 13th district court, issued the highest number of warrants and subpoenas with 799.
The fifty six district courts in Montana hear felony cases. It is the state’s general jurisdiction court hearing a large number of civil cases and all probate cases. The individual court can be located using the state’s judicial website. From there you can search for individual districts to get their clerk’s information.
The Montana Department of Justice provides a public background check in addition to their police criminal history records. Their background check includes felony charges, arrest and prosecution (RAP sheet) and misdemeanors. However, if you are looking for official full police reports, warrants, criminal court transcripts and field reports needs to be requested from the law enforcement agency or court directly. You can conduct a name based search, or a fingerprint based search which is more accurate. The name search is based just the dob, name and ssn. The federal search is different and is for statutorily authorized persons only.
You don't need to request a background check to see what the person was sentenced to. The Montana Department of Corrections provides free and public offender search that lets you see more than the sentence alone. In most cases you will see the photo of the offender, current status (ie on probation), which prison the individual is incarcerated, dates of sentence, offenses, which court, net sentence and more.