Filtering the output of an H-bridge
Sure there's a way to do it without inductors providing you are happy about not taking two much power from the H bridge to produce the sinewave. You can use RC low pass filters: -



If your PWM frequency is (say) 10kHz, after filtering with an RC filter having a 100Hz 3dB point you can calculate the attenuation at 20kHz by using the following calculator. I chose R = 160 ohms and C = 10uF.

The cut-off (3dB point) was 100 HZ and, from the graph it appears that 10 kHz is 40 dB down in amplitude.

Of course, knowledge about RC filters (1st order types) informs us that the amplitude rolls away at 20 dB per decade above the 3 dB point. Between 100 Hz and 10 kHz there are two decades of frequency hence a total of 40 dB (about 100:1 attenuation in terms of volts in and volts out).

You can use higher order filters made of RC networks too but you'll not get more than a few watts from this type of filter because of the resistors are in series with the signal.

The same page as the calculator as a host of other filter calculators