Consider the following capacitor here on Mouser (C1005C0G1H330J050BA). If my understanding is correct, the only power dissipated is due to the ESR - ideally, reactive elements dissipate no power (or is it no average power?).
The capacitor is 33pF rated at 50V. Let's suppose the frequency of interest is 915 MHz. Thus:
$$X_c = \frac{1}{2\pi f_c C} = \frac{1}{2\pi(915\times10^6)(33\times10^{-12})} = 5.271 \text{ }\Omega$$ $$I_{\text{peak}} = \frac{50 \text{ V}}{5.271 \text{ } \Omega} \approx 9.5 \text{ A}_{\text{peak}} \approx 6.72 \text{ A}_{\text{rms}}$$
If the current exceeds 6.72 A rms, the capacitor will be in bad shape. However, I would like to know if the capacitor can handle an RF power of +33 dBm (2 W)? My thinking is the following:
$$P = I^2 (ESR)$$
However, I only see the "low-ESR" claim and no actual number. Would this also depend on whether the capacitor was acting as a bypass or dc-blocking cap?