Constraining the long‐term variability and average of the Earth's magnetic field strength is fundamental to understanding the characteristics and behavior of the geomagnetic field. Questions remain about the strength of the average field, and the relationship between strength and reversal frequency, due to the dispersion of data from key time intervals. Here, we focus on the Cretaceous Normal Superchron (CNS; 121‐84 Ma), during which there were no reversals. We present new intensity results from 41 submarine basaltic glass (SBG) sites collected on the Nicoya Peninsula and Murcièlago Islands, Costa Rica. New and revised 40Ar/39Ar and biostratigraphic age constraints from previous studies indicate ages from 141 to 65 Ma. One site with an age of 135.1 ± 1.5 Ma (2σ) gave a reliable intensity result of 34 ± 8 µT (equivalent to a virtual axial dipole moment, VADM, value of 88 ± 20 ZAm2), three sites from 121 to 112 Ma, spanning the onset of the CNS, vary from 21 ± 1 to 34 ± 4 µT (53 ± 3 to 87 ± 10 ZAm2). These results from the CNS are all higher than the long‐term average of ∼42 ZAm2 and data from Suhongtu, Mongolia (46–53 ZAm2) and are similar to the Troodos Ophiolite, Cyprus (81 ZAm2, reinterpreted in this study). Together with the reinterpreted data, the new Costa Rica results suggest that the strength of the geomagnetic field was approximately the same both before and after the onset of the CNS. Therefore, the data do not support a strict correlation between polarity interval length and the strength of the magnetic field. Plain Language Summary Understanding the Earth's magnetic field behavior in the past is important to validate geodynamo simulations. However, because of the paucity of available data, it is poorly understood. In particular, it has been argued that the strength of the Earth's magnetic field, or paleointensity, was correlated with the stability of the field, where a strong field was less prone to magnetic reversals than a weak field. Hence, we have investigated the anomalously long period of stability, the Cretaceous Normal Superchron (CNS) during which no magnetic reversals occurred. Our new data from Costa Rican basaltic glasses, together with reinterpreted data from Inner Mongolia and the Troodos Ophiolite in Cyprus, suggest that the magnetic field during the CNS was similar to the present‐day field and these high values are nearly twice the long‐term average value for the last 200 Ma. However, high field values were also detected in the period prior to the onset of the CNS, hence our data do not support a strict correlation between strength and stability of the Earth's magnetic field. Key Points The Cretaceous Normal Superchron (CNS) is key to understanding geomagnetic field behavior We present new paleointensity data from Costa Rica over an age range of 135–112 Ma, spanning the onset of the CNS We find that field strength was high both prior and during the early CNS, which does not support a correlation between field strength and stability