Date: 202101
Local time of day: 1201-1800
Location: ZZZ.ARTCC, US
Weather elements / visibility: VMC
Aircraft: Small Transport; Low Wing; 2 Turbojet Eng
Operator: Air Carrier
Operating under: Part 135
Flight plan: IFR
Mission: Cargo / Freight / Delivery
Flight phase: Cruise
Airspace: Class A ZZZ
ATC / advisory: Center ZZZ
Reporter organization: Air Carrier
Reporter function: Pilot Flying; Captain
Reporter qualification: Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP)
Human factors: Communication Breakdown; Situational Awareness
Second reporter function: First Officer; Pilot Not Flying
Anomaly: ATC Issue All Types; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural FAR; Deviation / Discrepancy - Procedural Published Material / Policy
Detector: Person Air Traffic Control; Person Flight Crew
When detected: In-flight
Result: Air Traffic Control Issued New Clearance; Air Traffic Control Provided Assistance; Flight Crew Requested ATC Assistance / Clarification
Contributing factors: Environment - Non Weather Related; Human Factors
Primary problem: Environment - Non Weather Related

Narrative: At approximately XA:45; I realized it seemed to have been sometime since I had heard from the Controller. This is not entirely unusual. Due to the pandemic; there are times of much less radio chatter. In fact; several times a week; there are periods where nothing is said by anyone on frequency for lengths of time as long as 20-40 minutes save the occasional 'You still there?' It seemed to have been a bit longer than normal; so we called on our last assigned frequency. We heard nothing so I tried Guard and heard nothing. Unbeknownst to me the volume of the radio receiving Guard was accidentally turned down. As I was trying Guard my copilot found a frequency on the chart; made radio contact and was given the proper frequency we should be on. We re-established communication with ZZZ Center. All seemed fine; until the hand-off came with a phone number for possible pilot deviation.Upon arrival at our destination I called the number I had been given. The Controller I spoke with asked if I knew why I was given the number to call. I told him I believed it was due to lost radio contact. He said it was. We then discussed how this might have happened and things to do to re-establish radio contact. He then said it seemed to him we had never been given a hand-off. He also said that sector was very busy at the time the incident occurred. I have no doubt they were. I suspect they were even a bit understaffed due to the pandemic.  we concluded our conversation and thanked each other.My copilot and I spent considerable time discussing how this might have happened and how to prevent it in the future. But it must be noted there is no recourse for pilots that find themselves in this situation. There is also no sure way of completely preventing this type of situation. Pilots have no way of knowing when a hand-off should occur or when they have reached a specific time limit. Sometimes we check on; only to be immediately handed off with 'short stay; contact center on XYX.AB'. Other times we listen for long periods time listening to a completely silent radio. Those long periods of silence do not help at all. They only make the silence seem normal. Maybe controllers should be required to inform us; at check-on; how long or how many miles we can expect to be with them. They always seem to have an idea how long we will be in contact with them.


Second narrative: At approximately XA:45 local; at FL360; in cruise; we noticed that we hadn't heard from Center in quite some time.  During these times of COVID; it has become commonplace to go for long periods of time without hearing anything from Center or other traffic; especially in remote portions of the US. With the frequent occurrence that the only radio traffic heard is a pilot asking 'Still on?' just to make sure someone is still out there; it is impossible for a pilot to determine at what time/distance interval; he should be expecting contact; a hand-off; or any other instruction from ATC.This was the case on date.  During a long cross-country flight; we went for what seemed a long time without hearing anything from Center.  We acknowledged the fact and I keyed the mic to interrogate Center.  There was no response.  I tried again and even switched to the previous frequency; just in case.  Still no joy.  Pulled up the sectional to find the nearest Center and discovered ZZZ Center; Area X on frequency.  Called out to this Controller who brusquely inquired who we were; where we were; and informed us that we were on the wrong frequency; providing us with the correct one.  We immediately switched to the appropriate frequency; received a response and continued on our way.  Shortly thereafter; we received a call from Center that we had a possible pilot deviation and they had a number for us.  Number was copied; remainder of the flight continued without incident.Upon landing; we reached out to the Center phone number; who informed us that; after reviewing the recordings; we had not been handed off to the next sector; and it was no fault of ours.  Easy enough.  Controller called back a few minutes later; stating that the previous sector had filed a report on the incident; and needed pilot license number; etc.; for the reports.This brings me to the point where I ask; what can be done in this situation?  There is clearly no exact location where an aircraft is handed off to another sector/center/controller.  There is no exact amount of time flying through a sector before a switch is made.  What can we; as pilots; do to help with this situation?  Obviously; I cannot do my job as a pilot AND do the job of the controllers on the ground; so where is the happy medium?  Is there a guideline of the appropriate amount of time to go without hearing from ATC before inquiring?  Should we set a timer after each hand-off; or create a GPS way-point a certain distance down the line?It can be argued that 'I have a number for you to call; advise when ready to copy' are the most stressful 13 words heard in a pilot's day.  It generates fear; concern; trepidation and second guessing of the skills and abilities that we spend years honing and decades perfecting.  When we make mistakes; that is a definite way to bring attention to the problems and help find a solution.  What recourse do we have when a controller makes the mistake?  We spent the remainder of the flight and; arguably; the next 24 plus hours; stressing over what we should have done; when we should have checked in; how were we supposed to know; etc.


Synopsis: Air Taxi flight crew reported not hearing ATC for a while during cruise.  Reportedly; they had not been properly handed off to the next Center.