There is considerable controversy regarding the long‐term strength of continents (Te). While some authors obtain both low and high Te estimates from the Bouguer coherence and suggest that both crust and mantle contribute to lithospheric strength, others obtain estimates of only <25 km using the free‐air admittance and suggest that the mantle is weak. At the root of this controversy is how accurately Te can be recovered from coherence and admittance. We investigate this question by using synthetic topography and gravity anomaly data for which Te is known. We show that the discrepancies stem from comparison of theoretical curves to multitaper power spectral estimates of free‐air admittance. We reformulate the admittance method and show that it can recover synthetic Te estimates similar to those recovered using coherence. In light of these results, we estimate Te in Fennoscandia and obtain similar results using both techniques. Te is 20–40 km in the Caledonides, 40–60 km in the Swedish Svecofennides, 40–60 km in the Kola peninsula, and 70–100 km in southern Karelia and Svecofennian central Finland. Independent rheological modeling, using a xenolith‐controlled geotherm, predicts similar high Te in central Finland. Because Te exceeds crustal thickness in this area, the mantle must contribute significantly to the total strength. Te in Fennoscandia increases with tectonic age, seismic lithosphere thickness, and decreasing heat flow, and low Te correlates with frequent seismicity. However, in Proterozoic and Archean lithosphere the relationship of Te to age is ambiguous, suggesting that compositional variations may influence the strength of continents.