The docs recommend using try-catch for error handling, just as you would in synchronous code https://dart.dev/libraries/async/async-await#handling-errors
Additionally, if you need code to execute regardless of whether an exception occurs, wrap it in finally block https://dart.dev/language/error-handling#finally

Example:

try{
  var result = await someFuture();
  var result2 = await someFuture2();
  var result3 = await someFuture3();
}catch(e){
  print('Error: $e');
}finally{
   print('Done')
}