Magnetic nanoparticles dissipate heat when exposed to alternating magnetic fields (AMFs), making them suitable for cancer hyperthermia. Therapeutic heating applications demand accurate characterization of the heating power dissipated by the particles. Specific loss power (SLP) generated by magnetic nanoparticles is estimated from calorimetric heating measurements. Such measurements require adiabatic conditions, yet they are typically performed in an AMF device with non-adiabatic conditions. We have measured heating from four magnetic nanoparticle constructs using a range of frequencies (150-375 kHz) and magnetic fields (4-44 kA/m). We have extended a method developed to estimate SLP from the inherently non-adiabatic measurements, where we identify data ranges that conform to (quasi)-adiabatic conditions. Each time interval of measurement that met a predetermined criterion was used to generate a value of SLP, and the mean from all estimates was selected as the estimated SLP. Despite the application of rigorous selection criteria, measured temperature data displayed variability at specific heating loads resulting in larger variance of calculated mean SLP values. Overall, the results show a linear dependence of the SLP with AMF frequency, as anticipated by current models. Conversely, measured amplitude-dependent SLP profiles of all studied constructs conform to no predictions of current models.