We report spectral , imaging , and variability results from four new XMM-Newton  observations and two new Chandra  observations of high-redshift ( z \gtrsim 4 ) radio-loud quasars ( RLQs ) . Our targets span lower , and more representative , values of radio loudness than those of past samples of high-redshift RLQs studied in the X-ray regime . Our spectral analyses show power-law X-ray continua with a mean photon index , \langle \Gamma \rangle = 1.74 \pm 0.11 , that is consistent with measurements of lower redshift RLQs . These continua are likely dominated by jet-linked X-ray emission , and they follow the expected anti-correlation between photon index and radio loudness . We find no evidence of iron K \alpha emission lines or Compton-reflection continua . Our data also constrain intrinsic X-ray absorption in these RLQs . We find evidence for significant absorption ( N _ { H } \approx 1.7 \times 10 ^ { 22 } ~ { } \hbox { cm$ { } ^ { -2 } $ } ) in one RLQ of our sample ( SDSS J0011 + 1446 ) ; the incidence of X-ray absorption in our sample appears plausibly consistent with that for high-redshift RLQs that have higher values of radio loudness . In the Chandra  observation of PMN J2219 - 2719 we detect apparent extended ( \sim 14  kpc ) X-ray emission that is most likely due to a jet ; the X-ray luminosity of this putative jet is \approx 2 % that of the core . The analysis of a 4.9 GHz VLA image of PMN J2219 - 2719 reveals a structure that matches the X-ray extension found in this source . We also find evidence for long-term ( 450–460 days ) X-ray variability by 80–100 % in two of our targets .