We present a multiwavelength photometric and spectroscopic analysis of 13 super-Chandrasekhar-mass/2003fg-like Type Ia supernovae (SNe Ia). Nine of these objects were observed by the Carnegie Supernova Project. The 2003fg-like SNe have slowly declining light curves (
m15( B) < 1.3 mag), and peak absolute B-band magnitudes of 19 < M B< 21 mag. Many of the 2003fg-like SNe are located in the same part of the luminositywidth relation as normal SNe Ia. In the optical Band Vbands, the 2003fg-like SNe look like normal SNe Ia, but at redder wavelengths they diverge. Unlike other luminous SNe Ia, the 2003fg-like SNe generally have only one i-band maximum, which peaks after the epoch of the B-band maximum, while their near-IR (NIR) light-curve rise times can be 40 days longer than those of normal SNe Ia. They are also at least 1 mag brighter in the NIR bands than normal SNe Ia, peaking above M H= 19 mag, and generally have negative Hubble residuals, which may be the cause of some systematics in dark-energy experiments. Spectroscopically, the 2003fg-like SNe exhibit peculiarities such as unburnt carbon well past maximum light, a large spread (800012,000 km s1) in Si ii 6355 velocities at maximum light with no rapid early velocity decline, and no clear H-band break at +10 days. We find that SNe with a larger pseudo-equivalent width of C iiat maximum light have lower Si ii 6355 velocities and more slowly declining light curves. There are also multiple factors that contribute to the peak luminosity of 2003fg-like SNe. The explosion of a CO degenerate core inside a carbon-rich envelope is consistent with these observations. Such a configuration may come from the core-degenerate scenario.