In most cases, yes, though it depends on what tickets you received. Most traffic offenses can be paid online.
However, DUI type offenses (statute number 61-8-XXX), Driving While Suspended/Revoked, offenses with jail possible, and Careless Driving where the driver is under 25 years of age require personal appearance.
Additionally, by state law any "Title 45 offense" i.e., a charge with a statute number 45-X-XXX requires a person to personally appear, and then to be fingerprinted following their initial appearance.
For most other offenses, you may pay online at: http://citepayusa.com (VISA, MasterCard, Discover, Debit Card or echeck). You will need to select "Montana" then "pay a citation" then "Silver Bow County Justice Court." You always have the option to see a judge to discuss your case or to enter a not guilty plea. Online payments are merely a convenience for those who do not wish to dispute the charges against them.
In-person payments can be made at the Justice Court office : Room 305, 155 W. Granite Street, Butte, MT 59701, between the hours of 8:00 a.m. to 5:00 p.m. Check or cash only.