How should one assess model fit for non-linear regression?

I am looking at non linear regression. Below is some example output from a non linear regression using MATLAB. There are also two links below this output from the Minitab website. The links explain why for non linear regression $p$-values and the $R^2$ are not valid.

So my question is what should I look for in my results from a non linear regression? How can I tell if the overall model fit is reasonable & the coefficients are significant without using $p$-values and the $R^2$?

mdl =
Nonlinear regression model:
y ~ p1*cos(p2*xdata) + p2*sin(p1*xdata)

Estimated Coefficients:
Estimate             SE
p1      1.8818508110535      0.027430139389359
p2    0.700229815076442    0.00915260662357553

tStat               pValue
p1    68.6052223191956    2.26832562501304e-12
p2    76.5060538352836    9.49546284187105e-13

Number of observations: 10, Error degrees of freedom: 8
Root Mean Squared Error: 0.082
R-Squared: 0.996,  Adjusted R-Squared 0.995
F-statistic vs. zero model: 1.43e+03, p-value = 6.04e-11