Is there a power strip circuit breaker I can use to stop having to go to the basement when the microwave sometimes trips the circuit breaker?
No a power strip will likely not help. If your electrical circuit is properly installed, undamaged and being properly used then it should not trip. Even just a $5 breaker being repeatedly reset could damage the panel, resulting in a $1000 repair.
If you do get a power strip and it does trip before the electrical panel circuit breaker then it would likely be because the trip time-curve of the power strip is not designed to accommodate the power curve of the microwave, and you won't be fixing the problem, just delaying the inevitable, and possibly damaging the electronics of the microwave due to a disorganized power shutdown.
Residential "thermal-magnetic" breakers don't trip instantly at 20.1 amps. They are designed to trip under conditions that damage wiring, on an inverse time curve for thermal overload conditions, low overcurrents such as 1.5x the rating should trip between 90 and 300 seconds, 5x the rating should trip in 4 to 10 seconds, and a high magnetic inrush or short circuit of 10x or more they trip instantly.
For instance if you have a 1200 watt power hungry coffee maker and a 1800 watt microwave (actual ratings of my appliances) on the same circuit then you have 3000 watts on a 2400 watt circuit. (Code requires kitchen circuits be 20A, 20A x 120V = 2400 watts.) That 125% overload should hold for at least 5 minutes, and if it never trips it would still be within NEMA specs.
Those numbers really create a situation that a microwave tripping a breaker means some real circuit evaluation is necessary. Your microwave is faulty and drawing enormous overloads, a circuit breaker is failing, you have a loose connection that could cause arcing that could start a fire, or your combination of loads is greatly overloading your wires and repeated resetting and resuming abuse will create expensive repairs.
The breaker is safety device so you don't burn down the house. First I would figure out what else is on the circuit as it may be overload and if it is only the microwave then there is something wrong with the microwave if your wiring is up to par. In the US most wiring is either 12-2 or 14-2 in newer homes and can easily carry a 1200 watt load. Take incoming voltage: 120 volts Breaker AMP rating: 15 amps
120 x 15 = 1,800 Watts
So a basic circuit can carry safely 1,800 watts, look on your appliances that are connected to this circuit and they should be less than 1,800. There are other factors (wire length,material,etc) but keep it simple.
2nd - If the circuit blows and there is less than the 1,800 watts it may be a bad breaker, replace.
A microwave will use more than it's rated power, because nothing is 100% efficient, and some microwaves are less efficient than you might think. (The actual power usage should be on a sticker somewhere around the microwave door frame.) Also, a microwave will use even more power than that when first turning on, because it takes extra energy to start things up. (This is called the inrush current.)
Combined, this means that most microwaves really need a 20 amp circuit with no other high-current devices, and almost all of them will have a tendency to trip 15 amp breakers.
So, how big is your breaker?