This weekend, I had some time to run the Teensy RTC through it's paces. Here is some output, looks like sub-2PPM performance is possible. The sensor is a HTU21, I've also had good luck with the Si7021 sensor for humidity and temperature measurements. One of the key things is characterizing the performance of the crystal, and doing so slowly, so the sensor and the crystal are at the same temperature.

FWIW, I am manipulating the RTC_TCR register directly, seeking exhaustively for the solution with the smallest PPM error.

Welcome. Prepare to wait 18 seconds for CIC register to run out.

The predicted RTC error @ 28.33*C is: 3.6645PPM.

Best Combination: time constant divisor = 25, and PPM multiplier (j) =-3

Over a 76 second interval, Error measured: 14.13PPM for the MCU and 13.59PPM for the RTC, i.e. 0.54PPM.

The predicted RTC error @ 28.33*C is: 3.6645PPM.

Best Combination: time constant divisor = 25, and PPM multiplier (j) =-3

No change needed for RTC multiplier or time constant.

Over a 76 second interval, error measured: 14.13PPM for the MCU and 13.63PPM for the RTC, i.e. 0.50PPM.

The predicted RTC error @ 28.33*C is: 3.6645PPM.

No change needed for RTC multiplier or time constant.

Over a 76 second interval, error measured: 14.12PPM for the MCU and 13.76PPM for the RTC, i.e. 0.36PPM.

The predicted RTC error @ 28.59*C is: 3.5495PPM.

Best Combination: time constant divisor = 43, and PPM multiplier (j) =-5

Over a 130 second interval, error measured: 14.05PPM for the MCU and 13.57PPM for the RTC, i.e. 0.48PPM.

The predicted RTC error @ 28.54*C is: 3.5739PPM.

Best Combination: time constant divisor = 77, and PPM multiplier (j) =-9

Over a 232 second interval, error measured: 14.15PPM for the MCU and 13.26PPM for the RTC, i.e. 0.89PPM.

The predicted RTC error @ 24.33*C is: 4.8032PPM.

Best Combination: time constant divisor = 19, and PPM multiplier (j) =-3

Over a 58 second interval, error measured: 15.12PPM for the MCU and 14.66PPM for the RTC, i.e. 0.47PPM.

The predicted RTC error @ 22.99*C is: 4.9120PPM.

Best Combination: time constant divisor = 56, and PPM multiplier (j) =-9

Over a 169 second interval, error measured: 15.51PPM for the MCU and 15.52PPM for the RTC, i.e. -0.01PPM.

The predicted RTC error @ 19.81*C is: 4.6213PPM.

Best Combination: time constant divisor = 33, and PPM multiplier (j) =-5

Over a 100 second interval, error measured: 16.10PPM for the MCU and 16.08PPM for the RTC, i.e. 0.02PPM.

The predicted RTC error @ 18.29*C is: 4.2126PPM.

Best Combination: time constant divisor = 29, and PPM multiplier (j) =-4

Over a 88 second interval, error measured: 16.39PPM for the MCU and 16.32PPM for the RTC, i.e. 0.07PPM.

The predicted RTC error @ 17.20*C is: 3.8083PPM.

Best Combination: time constant divisor = 8, and PPM multiplier (j) =-1

Over a 25 second interval, error measured: 16.56PPM for the MCU and 16.12PPM for the RTC, i.e. 0.44PPM.

The predicted RTC error @ 16.92*C is: 3.6907PPM.

Best Combination: time constant divisor = 58, and PPM multiplier (j) =-7

Over a 175 second interval, error measured: 16.67PPM for the MCU and 16.91PPM for the RTC, i.e. -0.25PPM.

The predicted RTC error @ 15.33*C is: 2.9082PPM.

Best Combination: time constant divisor = 21, and PPM multiplier (j) =-2

Over a 64 second interval, Error measured: 16.92PPM for the MCU and 16.67PPM for the RTC, i.e. 0.25PPM.

The predicted RTC error @ 14.82*C is: 2.6132PPM.

Best Combination: time constant divisor = 35, and PPM multiplier (j) =-3

Over a 106 second interval, error measured: 17.00PPM for the MCU and 16.87PPM for the RTC, i.e. 0.13PPM.

The predicted RTC error @ 14.14*C is: 2.1953PPM.

Best Combination: time constant divisor = 139, and PPM multiplier (j) =-10

Over a 418 second interval, error measured: 17.15PPM for the MCU and 17.54PPM for the RTC, i.e. -0.39PPM.

The predicted RTC error @ 12.89*C is: 1.3270PPM.

Best Combination: time constant divisor = 23, and PPM multiplier (j) =-1

Over a 70 second interval, Error measured: 17.30PPM for the MCU and 16.91PPM for the RTC, i.e. 0.39PPM.

The predicted RTC error @ 12.73*C is: 1.2070PPM.

Best Combination: time constant divisor = 177, and PPM multiplier (j) =-7

Over a 532 second interval, error measured: 17.33PPM for the MCU and 17.20PPM for the RTC, i.e. 0.12PPM.

The predicted RTC error @ 12.40*C is: 0.9528PPM.

Best Combination: time constant divisor = 32, and PPM multiplier (j) =-1

Over a 97 second interval, error measured: 17.37PPM for the MCU and 16.95PPM for the RTC, i.e. 0.42PPM.

The predicted RTC error @ 12.31*C is: 0.8858PPM.

Best Combination: time constant divisor = 241, and PPM multiplier (j) =-7

Over a 724 second interval, error measured: 17.38PPM for the MCU and 17.05PPM for the RTC, i.e. 0.32PPM.

The predicted RTC error @ 12.37*C is: 0.9361PPM.

Success: time constant divisor (k)=163, and PPM multiplier (j) =-5

Over a 490 second interval, error measured: 17.38PPM for the MCU and 16.98PPM for the RTC, i.e. 0.40PPM.

The predicted RTC error @ 12.47*C is: 1.0109PPM.

Best Combination: time constant divisor = 151, and PPM multiplier (j) =-5

Over a 454 second interval, Error measured: 17.37PPM for the MCU and 16.93PPM for the RTC, i.e. 0.44PPM.

The predicted RTC error @ 12.61*C is: 1.1178PPM.

Best Combination: time constant divisor = 191, and PPM multiplier (j) =-7

Over a 574 second interval, error measured: 17.34PPM for the MCU and 16.87PPM for the RTC, i.e. 0.47PPM.

The predicted RTC error @ 12.84*C is: 1.2872PPM.

Best Combination: time constant divisor = 166, and PPM multiplier (j) =-7

Over a 499 second interval, error measured: 17.31PPM for the MCU and 16.87PPM for the RTC, i.e. 0.45PPM.

The predicted RTC error @ 12.99*C is: 1.3981PPM.

Best Combination: time constant divisor = 131, and PPM multiplier (j) =-6

Over a 394 second interval, error measured: 17.29PPM for the MCU and 16.85PPM for the RTC, i.e. 0.44PPM.

The predicted RTC error @ 13.09*C is: 1.4762PPM.

Best Combination: time constant divisor = 62, and PPM multiplier (j) =-3

Over a 187 second interval, error measured: 17.28PPM for the MCU and 16.85PPM for the RTC, i.e. 0.43PPM.

The predicted RTC error @ 13.08*C is: 1.4684PPM.

Best Combination: time constant divisor = 187, and PPM multiplier (j) =-9

Over a 562 second interval, error measured: 17.27PPM for the MCU and 16.80PPM for the RTC, i.e. 0.47PPM.

The predicted RTC error @ 24.70*C is: 4.7500PPM.

Best Combination: time constant divisor = 45, and PPM multiplier (j) =-7

Over a 136 second interval, Error measured: 14.93PPM for the MCU and 15.06PPM for the RTC, i.e. -0.13PPM.

The predicted RTC error @ 26.36*C is: 4.3787PPM.

Best Combination: time constant divisor = 7, and PPM multiplier (j) =-1

Over a 22 second interval, error measured: 14.64PPM for the MCU and 14.41PPM for the RTC, i.e. 0.23PPM.

The predicted RTC error @ 26.58*C is: 4.3121PPM.

Best Combination: time constant divisor = 71, and PPM multiplier (j) =-10

Over a 214 second interval, error measured: 14.45PPM for the MCU and 14.43PPM for the RTC, i.e. 0.02PPM.

The predicted RTC error @ 28.23*C is: 3.7109PPM.

Best Combination: time constant divisor = 74, and PPM multiplier (j) =-9

Over a 223 second interval, error measured: 14.10PPM for the MCU and 13.79PPM for the RTC, i.e. 0.30PPM.

The predicted RTC error @ 29.27*C is: 3.2235PPM.

Best Combination: time constant divisor = 85, and PPM multiplier (j) =-9

Over a 256 second interval, error measured: 13.86PPM for the MCU and 13.39PPM for the RTC, i.e. 0.47PPM.

The predicted RTC error @ 30.04*C is: 2.8084PPM.

Best Combination: time constant divisor = 87, and PPM multiplier (j) =-8

Over a 262 second interval, error measured: 13.70PPM for the MCU and 13.04PPM for the RTC, i.e. 0.66PPM.

The predicted RTC error @ 30.44*C is: 2.5774PPM.

Best Combination: time constant divisor = 71, and PPM multiplier (j) =-6

Over a 214 second interval, error measured: 13.61PPM for the MCU and 12.91PPM for the RTC, i.e. 0.71PPM.

The predicted RTC error @ 30.72*C is: 2.4012PPM.

Best Combination: time constant divisor = 89, and PPM multiplier (j) =-7

Over a 268 second interval, error measured: 13.55PPM for the MCU and 12.76PPM for the RTC, i.e. 0.79PPM.

The predicted RTC error @ 30.90*C is: 2.2938PPM.

Best Combination: time constant divisor = 133, and PPM multiplier (j) =-10

Over a 400 second interval, Error measured: 13.52PPM for the MCU and 12.65PPM for the RTC, i.e. 0.87PPM.