I completely understand your frustration. Having a probe thermometer give out right in the middle of a sear is stressful, especially with cuts like chicken breasts and thick pork chops that turn dry so quickly when overcooked.
While an instant-read thermometer is the only way to be completely certain, professional kitchen line cooks rely on a few reliable tactile methods when they cannot cut into the meat.
The most accurate tactile technique without slicing is the metal skewer or cake tester test. Insert a thin metal skewer or cake tester directly into the thickest part of the meat for about five seconds, then immediately pull it out and touch the tip to your lower lip or the inside of your wrist. For chicken breast, the metal should feel distinctly hot. For a modern thick pork chop, which is best enjoyed around medium doneness, the metal should feel warmly pleasant rather than scalding.
The second method is the firmness and bounce check using your fingertip. As proteins cook, muscle fibers contract and firm up. Chicken breast is done when it feels quite firm with a quick, resilient spring-back and no squishy give in the center. A juicy pork chop should offer gentle resistance with a slight bounce, similar to pressing the fleshy pad at the base of your thumb when your middle finger touches your thumb lightly.
Lastly, observe the juices. When you withdraw the skewer, any small bead of juice that rises to the surface should run clear and pale, not cloudy or tinted pink. Always be sure to rest the meat for about five minutes on a warm board so carryover cooking can gently finish bringing the center up to temperature before you plate it alongside your vegetables.