Citation X (C750)
Flight Crew Air Transport Pilot (ATP)
Fatigue; Situational Awareness
ATC Issue All Types; Deviation / Discrepancy - Procedural Clearance
Flight Crew Became Reoriented; Flight Crew Returned To Clearance
Human Factors
I was the flying pilot. We were in contact with Minneapolis Center and were issued a frequency change to a different sector. SIC made the frequency change and the female controller responded with something like '[callsign] Roger'. She was busy and there was other normal ATC chatter on the frequency that neither of us paid much attention to. After a little while I realized that I thought the controller had called herself 'Toledo Approach'; or possibly another 'Approach'. So we called and she said go back to our last assigned frequency. The controller on the last assigned frequency checked and by then we were in Chicago Center airspace and he gave us the correct frequency. After we checked in with Chicago that controller gave us a phone number for Minneapolis Center to call after we landed.I didn't think that we were out of communication more than 10-12 minutes but when I called and spoke with the person at Minneapolis Center he said we were NORDO for about 260 miles; or probably twice as long as I had thought.The only thing I would say to help the situation is better monitoring of the frequency on our part. A contributing factor was the response of the controller when we checked in on the incorrect frequency. She acknowledged the call but never told us that we had an incorrect frequency.  She was probably just so busy that she acknowledged us but then forgot about us as she was dealing with other traffic.We had started the day [very early]. Originally; when it first happened; I didn't think fatigue was a factor; but looking back it could have been.
[Report Narrative Contained No Additional Information.]
CE-750 flight crew reported they were off ATC frequency for about 260 miles when they copied an incorrect frequency.