We measure spin-down of the 59 ms X-ray pulsar Calvera by comparing the XMM-Newton discovery data from 2009 with new Chandra timing observations taken in 2013. Its period derivative isṖ = (3.19 ± 0.08) × 10 −15 , which corresponds to spin-down luminosityĖ = 6.1 × 10 35 erg s −1 , characteristic age τ c ≡ P /2Ṗ = 2.9 × 10 5 yr, and surface dipole magnetic field strength B s = 4.4 × 10 11 G. These values rule out a mildly recycled pulsar, but Calvera could be an orphaned central compact object (anti-magnetar), with a magnetic field that was initially buried by supernova debris and is now reemerging and approaching normal strength. We also performed unsuccessful searches for high-energy γ -rays from Calvera in both imaging and timing of >100 MeV Fermi photons. Even though the distance to Calvera is uncertain by an order of magnitude, an upper limit of d < 2 kpc inferred from X-ray spectra implies a γ -ray luminosity limit of <3.3 × 10 32 erg s −1 , which is less than that of any pulsar of comparableĖ. Calvera shares some properties with PSR J1740+1000, a young radio pulsar that we show by virtue of its lack of proper motion was born outside of the Galactic disk. As an energetic, high-Galactic-latitude pulsar, Calvera is unique in being undetected in both radio and γ -rays to faint limits, which should place interesting constraints on models for particle acceleration and beam patterns in pulsar magnetospheres.