We present novel surface-integral-equation formulations for efficient and accurate iterative solutions of electromagnetic problems involving zero-index (ZI) and near-zero-index (NZI) materials. When applied to materials with small permittivity and/or permeability values, conventional implementations employing traditional formulations tend to become inefficient, inaccurate, or both. Such numerical issues arise mainly due to low-frequency breakdowns related to inner problems, as well as due to deteriorating balance of inner and outer terms. By investigating formulations in limit cases, we develop novel formulations by properly balancing integral-equation operators. We show that the resulting formulations can provide efficient, accurate, and stable analysis of three-dimensional structures having ZI and NZI materials with arbitrarily small permittivity/permeability values.