We present a search for charged massive long-lived particles (CMLLPs) that are pair produced in $p\overline{p}$ collisions at $\sqrt{s}=1.96\text{ }\text{ }\mathrm{TeV}$ collected by the D0 experiment at the Fermilab Tevatron collider. Our result is a combination of two searches where either one or both CMLLPs are reconstructed in the detector. We select events with muonlike particles that have both speed and ionization energy loss ($\mathrm{d}E/\mathrm{d}x$) different from muons produced in $p\overline{p}$ collisions. In the absence of evidence for CMLLPs corresponding to $6.3\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of integrated luminosity, we set limits on the CMLLP masses in several supersymmetric models, excluding masses below 278 GeV for long-lived gaugino-like charginos, and masses below 244 GeV for long-lived Higgsino-like charginos at the 95% C.L. We also set limits on the cross section for pair production of long-lived scalar tau leptons that range from 0.04 to 0.008 pb for scalar tau lepton masses of 100--300 GeV.