Measurement of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>e</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>e</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:mo stretchy="false">→</mml:mo><mml:msup><mml:mi>K</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>K</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:math> cross section at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msqrt><mml:mi>s</mml:mi></mml:msqrt><mml:mo>=</mml:mo><mml:mn>2.00</mml:mn><mml:mtext> </mml:mtext><mml:mi>–</mml:mi><mml:mtext> </mml:mtext><mml:mn>3.08</mml:mn><mml:mtext> </mml:mtext><mml:mtext> </mml:mtext><mml:mi>GeV</mml:mi></mml:math>

The cross section of the process ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}}$ is measured at a number of center-of-mass energies $\sqrt{s}$ from 2.00 to 3.08 GeV with the BESIII detector at the Beijing Electron Positron Collider (BEPCII). The results provide the best precision achieved so far. A resonant structure around 2.2 GeV is observed in the cross section line shape. A Breit-Wigner fit yields a mass of $M=2239.2\ifmmode\pm\else\textpm\fi{}7.1\ifmmode\pm\else\textpm\fi{}11.3\text{ }\text{ }\mathrm{MeV}/{c}^{2}$ and a width of $\mathrm{\ensuremath{\Gamma}}=139.8\ifmmode\pm\else\textpm\fi{}12.3\ifmmode\pm\else\textpm\fi{}20.6\text{ }\text{ }\mathrm{MeV}$, where the first uncertainties are statistical and the second ones are systematic. In addition, the timelike electromagnetic form factor of the kaon is determined at the individual center-of-mass energy points.