(1) Background: Excessive body weight is a global problem in the 21st century. Children and adolescents, in particular, are at risk. Recently, there has been an increasing interest in the relationship between aerobic capacity and body composition. Therefore, this study aimed to determine the association between the individual parameters of cardiopulmonary capacity obtained in cardiopulmonary exercise testing (CPET) and selected parameters of body mass composition in high-BMI children and children over the 85th percentile according to the WHO growth reference. (2) Materials and Method: The research included 100 children of school-age (7–15 years) with an excessive BMI, i.e., over the 85th percentile as per the WHO Growth Reference (BMI percentile 95.21 ± 4.65; Z-score BMI: 2.07 ± 0.94). The study consisted of three parts: anthropometric measurements, measurement of body mass composition using a body composition analyzer (TANITA MC-780 S MA) using the bioimpedance method, and a cardiopulmonary exercise test on a pediatric cycle ergometer (Corival Pediatric, Lode BV) using the Godfrey protocol; (3) Results: The correlation between BMI and fat mass (FM) was very high (rho = 0.83; p = 0.00) with moderate body fat percentage (BF%) (rho = 0.48; p = 0.00). There was a relevant correlation between the amount of fat-free mass in total body mass and cardiopulmonary capacity expressed as the absolute aerobic capacity (VO2peak) (rho = 0.55; p = 0.00). (4) Conclusions: In the case of children and youth with higher BMI, there was a correlation between the amount of fat-free mass in total body mass and cardiopulmonary capacity in terms of absolute aerobic capacity.