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To find these examples we generalise work of Cremona--Freitas to give a candidate list of all congruences of a certain type between pairs of weight $2$ newforms $f \\in S_2^{\\mathrm{new}}(\\Gamma_0(N))$ and $g \\in S_2^{\\mathrm{new}}(\\Gamma_0(M))$ contained in the LMFDB (i.e., with $N, M \\leq 10\\,000$) and with coefficient fields of degree $\\leq 4$. 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To find these examples we generalise work of Cremona--Freitas to give a candidate list of all congruences of a certain type between pairs of weight $2$ newforms $f \\in S_2^{\\mathrm{new}}(\\Gamma_0(N))$ and $g \\in S_2^{\\mathrm{new}}(\\Gamma_0(M))$ contained in the LMFDB (i.e., with $N, M \\leq 10\\,000$) and with coefficient fields of degree $\\leq 4$. 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